# questions

tags: ['Physics', 'Wave Optics', 'BITSAT', 'BITSAT 2019']
source_db: MarksBatch2_P3.db
title:
two-monochromatic-light-waves-are-travelling-with-same-frequency-and-constant-phase-difference-if-both-waves-interfere-then

slug:
two-monochromatic-light-waves-are-travelling-with-same-frequency-and-constant-phase-difference-if-both-waves-interfere-then-75875

question:
<div class="question">Two monochromatic light waves are travelling with same frequency and constant phase difference. If both waves interfere, then</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">there is a gain of energy</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">there is a loss of energy</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">the energy is redistributed and the distribution remains constant in time</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">the energy is redistributed and the distribution changes with time</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">the energy is redistributed and the distribution remains constant in time</span> </div>

answer:
<div class="solution">When two waves with same frequency and constant phase difference interfere to each other, then after interference, intensity of resultant wave is distributed such that it is maximum at some points [constructive interference or bright fringes] and minimum at another points. [destructive interference or dark fringes]. Hence, energy is distributed and remains constant [in the form of bright and dark fringes]</div>


tags: ['Physics', 'Magnetic Effects of Current', 'BITSAT', 'BITSAT 2013']
source_db: MarksBatch2_P3.db
title:
two-parallel-conductors-carry-current-in-opposite-directions-as-shown-in-figure-one-conductor-carries-a-current-of-100-a-point-c-is-a-distance-2-d-to-

slug:
two-parallel-conductors-carry-current-in-opposite-directions-as-shown-in-figure-one-conductor-carries-a-current-of-100-a-point-c-is-a-distance-2-d-to-58915

question:
<div class="question">Two parallel conductors carry current in opposite directions as shown in figure. One conductor carries a current of $10.0 \mathrm{~A}$. Point $\mathrm{C}$ is a distance
<br/> <br/>$\frac{\mathrm{d}}{2}$ to the right of the $10.0 \mathrm{~A}$ current. If $\mathrm{d}=18 \mathrm{~cm}$ and I is adjusted so that the magnetic field at $\mathrm{Cis}$ zero, the value of the current $I$ is
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/RdRd2MV4dwY_55HYwA4zd3TvFOevZEZcgRkmRJagfQM.original.fullsize.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$10.0 \mathrm{~A}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$30.0 \mathrm{~A}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$8.0 \mathrm{~A}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$18.0 \mathrm{~A}$
<br/> <br/>#</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$30.0 \mathrm{~A}$</span> </div>

answer:
<div class="solution">The magnetic field at $\mathrm{C}$ due to first conductor
<br/> <br/>is $\mathrm{B}_{1}=\frac{\mu_{0}}{2 \pi} \frac{\mathrm{I}}{3 \mathrm{~d} / 2}$ (since, point $\mathrm{C}$ is separated
<br/> <br/>by $\mathrm{d}+\frac{\mathrm{d}}{2}=\frac{3 \mathrm{~d}}{2}$ from 1 st conductor). The direction of field is perpendicular to the plane of paper and directed outwards. The magnetic field at $\mathrm{C}$ due to second conductor is $\mathrm{B}_{2}=\frac{\mu_{0}}{2 \pi} \frac{10}{\mathrm{~d} / 2}$ (since, point $\mathrm{C}$
<br/> <br/>is separated by $\frac{\mathrm{d}}{2}$ from 2 nd conductor) The direction of field is perpendicular to the plane of paper and directed inwards. Since, direction of $\mathrm{B}_{1}$ and $\mathrm{B}_{2}$ at point $\mathrm{C}$ is in opposite direction and the magnetic field at C is zero, therefore,
<br/> <br/>$$
<br/> <br/>\begin{array}{c}
<br/> <br/>\mathrm{B}_{1}=\mathrm{B}_{2} \\
<br/> <br/>\frac{\mu_{0}}{2 \pi} \frac{\mathrm{I}}{3 \mathrm{~d} / 2}=\frac{\mu_{0}}{2 \pi} \frac{10}{\mathrm{~d} / 2}
<br/> <br/>\end{array}
<br/> <br/>$$
<br/> <br/>On solving $\mathrm{I}=30.0 \mathrm{~A}$</div>


tags: ['Physics', 'Oscillations', 'BITSAT', 'BITSAT 2014']
source_db: MarksBatch2_P3.db
title:
two-particles-p-and-q-describe-shm-of-same-amplitude-a-same-frequency-f-along-the-same-straight-line-the-maximum-distance-between-the-two-particles-is

slug:
two-particles-p-and-q-describe-shm-of-same-amplitude-a-same-frequency-f-along-the-same-straight-line-the-maximum-distance-between-the-two-particles-is-85917

question:
<div class="question">Two particles $\mathrm{P}$ and $\mathrm{Q}$ describe S.H.M. of same amplitude a, same frequency $\mathrm{f}$ along the same straight line. The maximum distance between the two particles is $\mathrm{a} \sqrt{2}$. The initial phase difference between the particle is $-$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">zero</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\pi / 2$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\pi / 6$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\pi \beta$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\pi / 2$</span> </div>

answer:
<div class="solution">$\mathrm{x}_{1}=\mathrm{a} \sin \left(\omega \mathrm{t}+\phi_{1}\right), \mathrm{x}_{2}=\mathrm{a} \sin \left(\omega \mathrm{t}+\phi_{2}\right)$
<br/> <br/>$\Rightarrow \quad\left|\mathrm{x}_{1}-\mathrm{x}_{2}\right|=2 \mathrm{a} \sin \left(\omega \mathrm{t}+\frac{\phi_{1}+\phi_{2}}{2}\right) \cos \left(\frac{\phi_{1}-\phi_{2}}{2}\right)$
<br/> <br/>Tomaximize $\left|\mathrm{x}_{1}-\mathrm{x}_{2}\right|: \sin \left(\omega \mathrm{t}+\frac{\phi_{1}+\phi_{2}}{2}\right)=1$
<br/> <br/>$\Rightarrow \mathrm{a} \sqrt{2}=2 \mathrm{a} \times 1 \times \cos \left(\frac{\phi_{1}-\phi_{2}}{2}\right)$
<br/> <br/>$\Rightarrow \frac{1}{\sqrt{2}}=\cos \left(\frac{\phi_{1}-\phi_{2}}{2}\right) \Rightarrow \frac{\pi}{4}=\frac{\phi_{1}-\phi_{2}}{2}$
<br/> <br/>$\Rightarrow \phi_{1}-\phi_{2}=\frac{\pi}{2}$</div>


tags: ['Physics', 'Magnetic Effects of Current', 'BITSAT', 'BITSAT 2015']
source_db: MarksBatch2_P3.db
title:
two-particles-x-and-y-having-equal-charges-after-being-accelerated-through-the-same-potential-difference-enter-a-region-of-uniform-magnetic-field-and-

slug:
two-particles-x-and-y-having-equal-charges-after-being-accelerated-through-the-same-potential-difference-enter-a-region-of-uniform-magnetic-field-and-11056

question:
<div class="question">Two particles $\mathrm{X}$ and $\mathrm{Y}$ having equal charges, after being accelerated through the same potential difference, enter a region of uniform magnetic field and describe circular paths of radii $\mathrm{R}_{1}$ and $\mathrm{R}_{2}$, respectively. The ratio of masses of $\mathrm{X}$ and $\mathrm{Y}$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\left(\mathrm{R}_{1} / \mathrm{R}_{2}\right)^{1 / 2}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\left(\mathrm{R}_{2} / \mathrm{R}_{1}\right)$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\left(\mathrm{R}_{1} / \mathrm{R}_{2}\right)^{2}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\left(\mathrm{R}_{1} / \mathrm{R}_{2}\right)$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\left(\mathrm{R}_{1} / \mathrm{R}_{2}\right)^{2}$</span> </div>

answer:
<div class="solution">When a charge particle is allowed to move in a uniform magnetic field, then it describes spiral or circular path
<br/> <br/>$$
<br/> <br/>\begin{array}{l}
<br/> <br/>\text { Centripetal force, } \frac{\mathrm{mv}^{2}}{\mathrm{R}}=\mathrm{qvB} \quad \therefore \\
<br/> <br/>\mathrm{v}=\left(\frac{\mathrm{qB}}{\mathrm{m}} \mathrm{R}\right) \\
<br/> <br/>\text { Hence, } \sqrt{\frac{2 \mathrm{q} \mathrm{V}}{\mathrm{m}}}=\left(\frac{\mathrm{qB}}{\mathrm{m}}\right) \mathrm{R}\left[\because \mathrm{V}=\sqrt{\frac{2 \mathrm{qV}}{\mathrm{m}}}\right] \\
<br/> <br/>\Rightarrow \mathrm{R}=\left(\frac{2 \mathrm{mV}}{\mathrm{q}}\right)^{1 / 2} \times \frac{1}{\mathrm{~B}} \\
<br/> <br/>\text { or, } \mathrm{m} \propto \mathrm{R}^{2}
<br/> <br/>\end{array}
<br/> <br/>$$
<br/> <br/>$[\because \mathrm{V}, \mathrm{q}$ and $\mathrm{B}$ are constant $]$
<br/> <br/>$$
<br/> <br/>\text { or, } \frac{\mathrm{m}_{1}}{\mathrm{~m}_{2}}=\left(\frac{\mathrm{R}_{1}}{\mathrm{R}_{2}}\right)^{2}
<br/> <br/>$$</div>


tags: ['Physics', 'Gravitation', 'BITSAT', 'BITSAT 2010']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">2</span> </div>
source_db: MarksBatch2_P3.db
title:
two-planets-a-and-b-have-the-same-material-density-if-the-radius-of-a-is-twice-that-of-b-then-the-ratio-of-the-escape-velocity-v-a-v-b-is

slug:
two-planets-a-and-b-have-the-same-material-density-if-the-radius-of-a-is-twice-that-of-b-then-the-ratio-of-the-escape-velocity-v-a-v-b-is-41238

question:
<div class="question">Two planets $\mathrm{A}$ and $\mathrm{B}$ have the same material density. If the radius of $\mathrm{A}$ is twice that of $\mathrm{B}$, then the ratio of the escape velocity $\mathrm{v}_{\mathrm{A}} / \mathrm{v}_{\mathrm{B}}$ is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">2</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\sqrt{2}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$1 / \sqrt{2}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$1 / 2$</span> </li> </ul>

answer:
<div class="solution">$v_{e}=\sqrt{2 g R}=\sqrt{\frac{2 G M}{R^{2}}} R=\sqrt{\frac{2 G d \frac{4}{3} \pi R^{3}}{R^{2}}} R$<br/>$=\mathrm{R} \sqrt{2 \mathrm{Gd} \frac{4}{3} \pi}$<br/>as $v_{e} \propto R$ for same density, $\frac{v_{A}}{v_{B}}=2$</div>


tags: ['Physics', 'Gravitation', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$3: 4$</span> </div>
source_db: MarksBatch2_P3.db
title:
two-planets-a-and-b-of-radii-r-and-15-r-have-densities-and-2-respectively-the-ratio-of-acceleration-due-to-gravity-at-the-surface-of-b-to-a-is

slug:
two-planets-a-and-b-of-radii-r-and-15-r-have-densities-and-2-respectively-the-ratio-of-acceleration-due-to-gravity-at-the-surface-of-b-to-a-is-71448

question:
<div class="question">Two planets $A$ and $B$ of radii $R$ and $1.5 R$ have densities $\rho$ and $\rho / 2$ respectively. The ratio of acceleration due to gravity at the surface of $B$ to A is :</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$2: 3$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$2: 1$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$3: 4$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$4: 3$</span> </li> </ul>

answer:
<div class="solution">Acceleration due to gravity,<br/>$\mathrm{g}=\frac{\mathrm{GM}}{\mathrm{R}^2}=\frac{4}{3} \pi \mathrm{G} \rho \mathrm{R}$<br/>$\therefore \frac{g_2}{g_1}=\frac{\rho_2}{\rho_1} \times \frac{R_2}{R_1}=\frac{1}{2} \times 1.5=\frac{3}{4}$</div>


tags: ['Physics', 'Electrostatics', 'BITSAT', 'BITSAT 2014']
source_db: MarksBatch2_P3.db
title:
two-point-dipoles-p-k-and-2-p-k-are-located-at-000-and-1-m-0-2-m-respectively-the-resultant-electric-field-due-to-the-two-dipoles-at-the-point-1-m-0-0

slug:
two-point-dipoles-p-k-and-2-p-k-are-located-at-000-and-1-m-0-2-m-respectively-the-resultant-electric-field-due-to-the-two-dipoles-at-the-point-1-m-0-0-84590

question:
<div class="question">Two point dipoles $\mathrm{p} \hat{\mathrm{k}}$ and $\frac{\mathrm{p}}{2} \hat{\mathrm{k}}$ are located at (0,0,0) and $(1 \mathrm{~m}, 0,2 \mathrm{~m})$ respectively. The resultant electric field due to the two dipoles at the point $(1 \mathrm{~m}, 0,0)$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{9 \mathrm{p}}{32 \pi \epsilon_{0}} \hat{\mathrm{k}}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{-7 \mathrm{p}}{32 \pi \epsilon_{0}} \hat{\mathrm{k}}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{7 \mathrm{p}}{32 \pi \epsilon_{0}} \hat{\mathrm{k}}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of these</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{-7 \mathrm{p}}{32 \pi \epsilon_{0}} \hat{\mathrm{k}}$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/YgVh4Z41MPZDma9TbgAGMNjjHrJwf_jNINKRm8wVk1c.original.fullsize.png"/><br/> <br/> <br/>The given point is at axis of $\frac{\overrightarrow{\mathrm{P}}}{2}$ dipole and
<br/> <br/>at equatorial line of $\overrightarrow{\mathrm{P}}$ dipole so that field at given point.</div>


tags: ['Physics', 'Motion In Two Dimensions', 'BITSAT', 'BITSAT 2010']
source_db: MarksBatch2_P3.db
title:
two-projectiles-a-and-b-are-thrown-with-the-same-speed-but-angles-are-4-0-and-5-0-with-the-horizontal-then

slug:
two-projectiles-a-and-b-are-thrown-with-the-same-speed-but-angles-are-4-0-and-5-0-with-the-horizontal-then-32029

question:
<div class="question">Two projectiles $\mathrm{A}$ and $\mathrm{B}$ are thrown with the same speed but angles are $40^{\circ}$ and $50^{\circ}$ with the horizontal. Then</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">A will fall earlier</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{B}$ will fall earlier</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">both will fall at the same time</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of these</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">A will fall earlier</span> </div>

answer:
<div class="solution">$\mathrm{T}=\frac{2 \mathrm{u} \sin \theta}{\mathrm{g}},$ lesser is the value of $\theta$, lesser is $\sin \theta$ and hence lesser will be the time taken. Hence A will fall earlier.</div>


tags: ['Physics', 'Nuclear Physics', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 2)']
source_db: MarksBatch2_P3.db
title:
two-radioactive-elements-a-and-b-initially-have-same-number-of-atoms-the-half-life-of-a-is-same-as-the-average-life-of-b-if-a-and-b-are-decay-constant-1

slug:
two-radioactive-elements-a-and-b-initially-have-same-number-of-atoms-the-half-life-of-a-is-same-as-the-average-life-of-b-if-a-and-b-are-decay-constant-1-57202

question:
<div class="question">Two radioactive elements $A$ and $B$ initially have same number of atoms. The half life of $A$ is same as the average life of $B$. If $\lambda_A$ and $\lambda_B$ are decay constants of $A$ and $B$ respectively, then choose the correct relation from the given options.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\lambda_A=\lambda_B$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\lambda_A=2 \lambda_B$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\lambda_{\mathrm{A}}=\lambda_{\mathrm{B}} \ln 2$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\lambda_{\mathrm{A}} \ln 2=\lambda_{\mathrm{B}}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\lambda_{\mathrm{A}}=\lambda_{\mathrm{B}} \ln 2$</span> </div>

answer:
<div class="solution">It is given that<br/>$\begin{aligned}<br/>&amp; \left(\frac{\mathrm{T}_1}{2}\right)_{\mathrm{A}}=\left(\mathrm{T}_{\mathrm{av}}\right)_{\mathrm{B}} \\<br/>&amp; \because \mathrm{T}_{1 / 2}=\frac{\ell \mathrm{n} 2}{\lambda} \text { and } \mathrm{T}_{\mathrm{av}}=\frac{1}{\lambda} \\<br/>&amp; \therefore \frac{\ell \mathrm{n} 2}{\lambda_{\mathrm{A}}}=\frac{1}{\lambda_{\mathrm{B}}} \Rightarrow \lambda_{\mathrm{A}}=\lambda_{\mathrm{B}} \ell n 2<br/>\end{aligned}$</div>


tags: ['Physics', 'Mathematics in Physics', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 2)']
source_db: MarksBatch2_P3.db
title:
two-resistances-are-given-as-r-1-10-05-and-r-2-15-05-the-percentage-error-in-the-measurement-of-equivalent-resistance-when-they-are-connected-in-paral

slug:
two-resistances-are-given-as-r-1-10-05-and-r-2-15-05-the-percentage-error-in-the-measurement-of-equivalent-resistance-when-they-are-connected-in-paral-98190

question:
<div class="question">Two resistances are given as $R_1=(10 \pm$ $0.5) \Omega$ and $R_2=(15 \pm 0.5) \Omega$. The percentage error in the measurement of equivalent resistance when they are connected in parallel is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>6.33</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>2.33</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>4.33</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>5.33</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>4.33</span> </div>

answer:
<div class="solution">Equivalent resistance in parallel combination is given by<br/>$\begin{aligned}<br/>&amp; \frac{1}{R_{\text {eq }}}=\frac{1}{R_1}+\frac{1}{R_2} \\<br/>&amp; \Rightarrow R_{\text {eq }}=\frac{R_1 R_2}{R_1+R_2}=\frac{10 \times 15}{10+15}=6<br/>\end{aligned}$<br/>Differentiating both sides, we get<br/>$\begin{aligned} &amp; \frac{\Delta R_{\text {eq }}}{\mathrm{R}_{\mathrm{eq}}^2}=\frac{\Delta \mathrm{R}_1}{\mathrm{R}_1^2}+\frac{\Delta \mathrm{R}_2}{\mathrm{R}_2^2} \\ &amp; \Rightarrow \frac{\Delta \mathrm{R}_{\mathrm{eq}}}{\mathrm{R}_{\mathrm{eq}}}=\left(\frac{\Delta \mathrm{R}_1}{\mathrm{R}_1^2}+\frac{\Delta \mathrm{R}_2}{\mathrm{R}_2^2}\right) \mathrm{R}_{\mathrm{eq}} \\ &amp; =\left(\frac{0.5}{100}+\frac{0.5}{225}\right) \cdot 6=\left(\frac{6 \times 0.5}{25}\right)\left(\frac{1}{4}+\frac{1}{9}\right)=\frac{13}{300} \\ &amp; \frac{\Delta \mathrm{R}_{\mathrm{eq}}}{\mathrm{R}_{\mathrm{eq}}} \times 100=\frac{13}{3}=4.33 \%\end{aligned}$</div>


tags: ['Physics', 'Current Electricity', 'BITSAT', 'BITSAT 2016']
source_db: MarksBatch2_P3.db
title:
two-resistances-at-0-c-with-temperature-coefficient-of-resistance-1-and-2-joined-in-series-act-as-a-single-resistance-in-a-circuit-the-temperature-coe

slug:
two-resistances-at-0-c-with-temperature-coefficient-of-resistance-1-and-2-joined-in-series-act-as-a-single-resistance-in-a-circuit-the-temperature-coe-86102

question:
<div class="question">Two resistances at $0^{\circ} \mathrm{C}$ with temperature coefficient of resistance $\alpha_{1}$ and $\alpha_{2}$ joined in series act as a single resistance in a circuit. The temperature coefficient of their single resistance will be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\alpha_{1}+\alpha_{2}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{\alpha_{1} \alpha_{2}}{\alpha_{1}+\alpha_{2}}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{\alpha_{1}-\alpha_{2}}{2}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\frac{\alpha_{1}+\alpha_{2}}{2}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{\alpha_{1}+\alpha_{2}}{2}$</span> </div>

answer:
<div class="solution">$\begin{aligned} R_{1} &amp;=R_{0}\left(1+\alpha_{1} t\right)+R_{0}\left(1+\alpha_{2} t\right) \\ &amp;=2 R_{0}\left(1+\frac{\alpha_{1}+\alpha_{2}}{2} t\right) \end{aligned}$
<br/> <br/>Comparing with $R=R_{0}(1+\alpha t)$
<br/> <br/>$\alpha=\frac{\alpha_{1}+\alpha_{2}}{2}$</div>


tags: ['Physics', 'Rotational Motion', 'JEE Main']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">2</span> </div>
source_db: MarksBatch2_P3.db
title:
two-rings-of-radius-r-and-nr-made-of-same-material-have-the-ratio-of-moment-of-inertia-about-an-axis-passing-through-centre-is-1-8-the-value-of-n-is-1

slug:
two-rings-of-radius-r-and-nr-made-of-same-material-have-the-ratio-of-moment-of-inertia-about-an-axis-passing-through-centre-is-1-8-the-value-of-n-is-1-54744

question:
<div class="question">Two rings of radius $\mathrm{R}$ and $\mathrm{nR}$ made of same material have the ratio of moment of inertia about an axis passing through centre is 1: 8 . The value of $\mathrm{n}$ is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">2</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$2 \sqrt{2}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">4</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$1 / 2$</span> </li> </ul>

answer:
<div class="solution">Ratio of moment of inertia of the rings
<br/> <br/>$$
<br/> <br/>\frac{\mathrm{I}_{1}}{\mathrm{I}_{2}}=\left(\frac{\mathrm{M}_{1}}{\mathrm{M}_{2}}\right)\left(\frac{\mathrm{R}_{1}}{\mathrm{R}_{2}}\right)^{2}
<br/> <br/>$$
<br/> <br/>$\begin{aligned}=&amp;\left(\frac{\lambda l_{1}}{\lambda l_{2}}\right)\left(\frac{R_{1}}{R_{2}}\right)^{2}=\left(\frac{2 \pi \mathrm{R}}{2 \pi \mathrm{n} \mathrm{R}}\right)\left(\frac{\mathrm{R}}{\mathrm{n} \mathrm{R}}\right)^{2} \\ &amp;(\lambda=\text { linear density of wire }=\mathrm{constant}) \\ \Rightarrow \quad \frac{\mathrm{I}_{1}}{\mathrm{I}_{2}}=\frac{1}{\mathrm{n}^{3}}=\frac{1}{8} \quad \text { (given) } \\ \therefore \quad \mathrm{n}^{3}=8 \Rightarrow \mathrm{n}=2 \end{aligned}$
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/JkVmSEPvkfJzbUYQif1yY1la2j2rfWcNpzIF3syUIzU.original.fullsize.png"/></div>


tags: ['Physics', 'Rotational Motion', 'BITSAT', 'BITSAT 2013']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">2</span> </div>
source_db: MarksBatch2_P3.db
title:
two-rings-of-radius-r-and-nr-made-of-same-material-have-the-ratio-of-moment-of-inertia-about-an-axis-passing-through-centre-is-1-8-the-value-of-n-is

slug:
two-rings-of-radius-r-and-nr-made-of-same-material-have-the-ratio-of-moment-of-inertia-about-an-axis-passing-through-centre-is-1-8-the-value-of-n-is-53166

question:
<div class="question">Two rings of radius $\mathrm{R}$ and $\mathrm{nR}$ made of same material have the ratio of moment of inertia about an axis passing through centre is 1: 8 . The value of $\mathrm{n}$ is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">2</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$2 \sqrt{2}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">4</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$1 / 2$</span> </li> </ul>

answer:
<div class="solution">Ratio of moment of inertia of the rings
<br/> <br/>$$
<br/> <br/>\frac{\mathrm{I}_{1}}{\mathrm{I}_{2}}=\left(\frac{\mathrm{M}_{1}}{\mathrm{M}_{2}}\right)\left(\frac{\mathrm{R}_{1}}{\mathrm{R}_{2}}\right)^{2}
<br/> <br/>$$
<br/> <br/>$\begin{aligned}=&amp;\left(\frac{\lambda l_{1}}{\lambda l_{2}}\right)\left(\frac{R_{1}}{R_{2}}\right)^{2}=\left(\frac{2 \pi \mathrm{R}}{2 \pi \mathrm{n} \mathrm{R}}\right)\left(\frac{\mathrm{R}}{\mathrm{n} \mathrm{R}}\right)^{2} \\ &amp;(\lambda=\text { linear density of wire }=\mathrm{constant}) \\ \Rightarrow \quad \frac{\mathrm{I}_{1}}{\mathrm{I}_{2}}=\frac{1}{\mathrm{n}^{3}}=\frac{1}{8} \quad \text { (given) } \\ \therefore \quad \mathrm{n}^{3}=8 \Rightarrow \mathrm{n}=2 \end{aligned}$
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/JkVmSEPvkfJzbUYQif1yY1la2j2rfWcNpzIF3syUIzU.original.fullsize.png"/></div>


tags: ['Physics', 'Mechanical Properties of Fluids', 'BITSAT', 'BITSAT 2019']
source_db: MarksBatch2_P3.db
title:
two-separate-soap-bubbles-of-radii-3-10-3-m-and-2-10-3-m-respectively-formed-of-same-liquid-surface-tension-65-10-2-n-m-1-come-together-to-form-a-doub

slug:
two-separate-soap-bubbles-of-radii-3-10-3-m-and-2-10-3-m-respectively-formed-of-same-liquid-surface-tension-65-10-2-n-m-1-come-together-to-form-a-doub-82995

question:
<div class="question">Two separate soap bubbles of radii <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo> </mo><mi mathvariant="normal">m</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo> </mo><mi mathvariant="normal">m</mi></math> respectively, formed of same liquid (surface tension <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>65</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>2</mn></mrow></msup><mo> </mo><mi mathvariant="normal">N</mi><mo> </mo><msup><mi mathvariant="normal">m</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>) come together to form a double bubble. The radius of interface of double bubble is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo> </mo><mi mathvariant="normal">m</mi></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo> </mo><mi mathvariant="normal">m</mi></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo> </mo><mi mathvariant="normal">m</mi></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>66</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo> </mo><mi mathvariant="normal">m</mi></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo> </mo><mi mathvariant="normal">m</mi></math></span> </div>

answer:
<div class="solution"><p>Excess pressure inside first bubble of radius <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>r</mi><mn>1</mn></msub></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mn>1</mn></msub><mo>=</mo><msub><mi>p</mi><mn>0</mn></msub><mo>+</mo><mfrac><mrow><mn>4</mn><mi>T</mi></mrow><msub><mi>r</mi><mn>1</mn></msub></mfrac></math></p><p>Excess pressure inside second bubble of radius <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>r</mi><mn>2</mn></msub></math><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>p</mi><mn>2</mn></msub><mo>=</mo><msub><mi>p</mi><mn>0</mn></msub><mo>+</mo><mfrac><mrow><mn>4</mn><mi>T</mi></mrow><msub><mi>r</mi><mn>2</mn></msub></mfrac></math></p><p>Excess pressure inside double bubble,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><msub><mi>p</mi><mn>2</mn></msub><mo>-</mo><msub><mi>p</mi><mn>1</mn></msub></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mn>4</mn><mi>T</mi><mfenced><mfrac><mrow><msub><mi>r</mi><mn>1</mn></msub><mo>-</mo><msub><mi>r</mi><mn>2</mn></msub></mrow><mrow><msub><mi>r</mi><mn>1</mn></msub><msub><mi>r</mi><mn>2</mn></msub></mrow></mfrac></mfenced></math></p><p>If <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math> be the radius of double bubble, then</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mfrac><mrow><mn>4</mn><mi>T</mi></mrow><mi>R</mi></mfrac></math></p><p>or <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mi>T</mi><mfenced><mfrac><mrow><msub><mi>r</mi><mn>1</mn></msub><mo>-</mo><msub><mi>r</mi><mn>2</mn></msub></mrow><mrow><msub><mi>r</mi><mn>1</mn></msub><msub><mi>r</mi><mn>2</mn></msub></mrow></mfrac></mfenced><mo>=</mo><mfrac><mrow><mn>4</mn><mi>T</mi></mrow><mi>R</mi></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mi>R</mi><mo>=</mo><mfrac><mrow><msub><mi>r</mi><mn>1</mn></msub><msub><mi>r</mi><mn>2</mn></msub></mrow><mrow><msub><mi>r</mi><mn>1</mn></msub><mo>-</mo><msub><mi>r</mi><mn>2</mn></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>3</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo>×</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup></mrow><mrow><mfenced><mrow><mn>3</mn><mo>-</mo><mn>2</mn></mrow></mfenced><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup></mrow></mfrac><mo>=</mo><mn>6</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo> </mo><mi mathvariant="normal">m</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mn>6</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo> </mo><mi mathvariant="normal">m</mi></math></p></div>


tags: ['Physics', 'Oscillations', 'BITSAT', 'BITSAT 2017']
source_db: MarksBatch2_P3.db
title:
two-simple-pendulums-of-lengths-5-m-and-20-m-respectively-are-given-small-displacement-in-one-direction-at-the-same-time-they-will-again-be-in-the-sam

slug:
two-simple-pendulums-of-lengths-5-m-and-20-m-respectively-are-given-small-displacement-in-one-direction-at-the-same-time-they-will-again-be-in-the-sam-46770

question:
<div class="question">Two simple pendulums of lengths <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo> </mo><mi mathvariant="normal">m</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo> </mo><mi mathvariant="normal">m</mi></math> respectively are given small displacement in one direction at the same time they will again be in the same sense when the pendulum of shorter length has completed <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math> oscillations. Then, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math> is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></span> </li> </ul>

answer:
<div class="solution"><p>According to question</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>n</mi><mn>1</mn></msub><msub><mi>T</mi><mn>1</mn></msub><mo>=</mo><msub><mi>n</mi><mn>2</mn></msub><msub><mi>T</mi><mn>2</mn></msub></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo> </mo><mi>n</mi><mo>·</mo><mn>2</mn><mi>π</mi><msqrt><mfrac><mn>5</mn><mi>g</mi></mfrac></msqrt><mo>=</mo><mfenced><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mn>2</mn><mi>π</mi><msqrt><mfrac><mn>20</mn><mi>g</mi></mfrac></msqrt></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>n</mi><mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow></mfrac><mo>=</mo><mn>2</mn><mo>⇒</mo><mi>n</mi><mo>=</mo><mn>2</mn></math></p></div>


tags: ['Physics', 'Electromagnetic Induction', 'BITSAT', 'BITSAT 2010']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">1: 2</span> </div>
source_db: MarksBatch2_P3.db
title:
two-solenoids-of-same-crosssectional-area-have-their-lengths-and-number-of-turns-in-ratio-of-1-2-the-ratio-of-selfinductance-of-two-solenoids-is

slug:
two-solenoids-of-same-crosssectional-area-have-their-lengths-and-number-of-turns-in-ratio-of-1-2-the-ratio-of-selfinductance-of-two-solenoids-is-85011

question:
<div class="question">Two solenoids of same cross-sectional area have their lengths and number of turns in ratio of 1: 2 . The ratio of self-inductance of two solenoids is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">1: 1</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">1: 2</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">2: 1</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">1: 4</span> </li> </ul>

answer:
<div class="solution">From $L=\frac{\mu_{0} N^{2} A}{1} \alpha \frac{N^{2}}{1}$<br/>we get, $\frac{\mathrm{L}_{1}}{\mathrm{~L}_{2}}=\frac{(1 / 2)^{2}}{1 / 2}=\frac{1}{2}$</div>


tags: ['Physics', 'Waves and Sound', 'BITSAT', 'BITSAT 2019']
source_db: MarksBatch2_P3.db
title:
two-sources-of-sound-a-and-b-are-moving-towards-and-away-from-a-stationary-observer-with-the-same-speed-respectively-if-the-frequency-of-the-sound-pro

slug:
two-sources-of-sound-a-and-b-are-moving-towards-and-away-from-a-stationary-observer-with-the-same-speed-respectively-if-the-frequency-of-the-sound-pro-96602

question:
<div class="question">Two sources of sound <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math> are moving towards and away from a stationary observer with the same speed respectively. If the frequency of the sound produced by both the sources is equal to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>400</mn><mo> </mo><mi>Hz</mi></math>, then the speed of sources (approximately) if the observer detects 4 beats per second, is [Given, speed of sound <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>340</mn><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>]</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>7</mn><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>.</mo><mn>4</mn><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>4</mn><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>7</mn><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></span> </div>

answer:
<div class="solution"><p>Given, frequency of sound produced by sources <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>f</mi><mi>A</mi></msub><mo>=</mo><msub><mi>f</mi><mi>B</mi></msub><mo>=</mo><mn>400</mn><mo> </mo><mi>Hz</mi></math></p><p>Speed of sound in air, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mn>340</mn><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></p><p>Apparent frequency heard by the observer when source <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math> is moving towards him,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi>f</mi><mi>A</mi><mo>'</mo></msubsup><mo>=</mo><mfrac><mi>v</mi><mrow><mi>v</mi><mo>-</mo><msub><mi>v</mi><mi>S</mi></msub></mrow></mfrac><mo>×</mo><msub><mi>f</mi><mi>A</mi></msub><mo>=</mo><mfrac><mn>340</mn><mrow><mn>340</mn><mo>-</mo><msub><mi>v</mi><mi>S</mi></msub></mrow></mfrac><mo>×</mo><mn>400</mn></math></p><p>Apparent frequency heard by the observer when source <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math> is moving away from him,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi>f</mi><mi>B</mi><mo>'</mo></msubsup><mo>=</mo><mfrac><mi>v</mi><mrow><mi>v</mi><mo>+</mo><msub><mi>v</mi><mi>s</mi></msub></mrow></mfrac><mo>×</mo><msub><mi>f</mi><mi>B</mi></msub><mo>=</mo><mfrac><mn>340</mn><mrow><mn>340</mn><mo>+</mo><msub><mi>v</mi><mi>s</mi></msub></mrow></mfrac><mo>×</mo><mn>400</mn></math></p><p>Given, Beats <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><msubsup><mi>f</mi><mi>A</mi><mo>'</mo></msubsup><mo>-</mo><msubsup><mi>f</mi><mi>B</mi><mo>'</mo></msubsup><mo>=</mo><mn>4</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>340</mn><mrow><mn>340</mn><mo>-</mo><msub><mi>v</mi><mi>s</mi></msub></mrow></mfrac><mo>×</mo><mn>400</mn><mo>-</mo><mfrac><mn>340</mn><mrow><mn>340</mn><mo>+</mo><msub><mi>v</mi><mi>s</mi></msub></mrow></mfrac><mo>×</mo><mn>400</mn><mo>=</mo><mn>4</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mfrac><mrow><mn>34000</mn><mo>×</mo><mn>2</mn><msub><mi>v</mi><mi>S</mi></msub></mrow><mrow><msup><mn>340</mn><mn>2</mn></msup><mo>-</mo><msubsup><mi>v</mi><mi>S</mi><mn>2</mn></msubsup></mrow></mfrac><mo>=</mo><mn>1</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>34000</mn><mo>×</mo><mn>2</mn><msub><mi>v</mi><mi>S</mi></msub></mrow><msup><mn>340</mn><mn>2</mn></msup></mfrac><mo>=</mo><mn>1</mn></math>   <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>∵</mo><mo> </mo><msubsup><mi>v</mi><mi>S</mi><mn>2</mn></msubsup><mo>&lt;</mo><mo>&lt;</mo><msup><mn>340</mn><mn>2</mn></msup></mrow></mfenced></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><msub><mi>v</mi><mi>s</mi></msub><mo>=</mo><mn>1</mn><mo>.</mo><mn>7</mn><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></p></div>


tags: ['Physics', 'Thermal Properties of Matter', 'BITSAT', 'BITSAT 2016']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">8: 25</span> </div>
source_db: MarksBatch2_P3.db
title:
two-spheres-of-different-materials-one-with-double-the-radius-and-onefourth-wall-thickness-of-the-other-are-filled-with-ice-if-the-time-taken-for-comp

slug:
two-spheres-of-different-materials-one-with-double-the-radius-and-onefourth-wall-thickness-of-the-other-are-filled-with-ice-if-the-time-taken-for-comp-79415

question:
<div class="question">Two spheres of different materials one with double the radius and one-fourth wall thickness of the other are filled with ice. If the time taken for complete melting of ice in the larger sphere is 25 minute and for smaller one is 16 minute, the ratio of thermal conductivities of the materials of larger spheres to that of smaller sphere is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">4: 5</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">5: 4</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">25: 8</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">8: 25</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

answer:
<div class="solution">Radius of small sphere $=\mathrm{r}$ Thickness of small sphere $=\mathrm{t}$ Radius of bigger sphere $=2 \mathrm{r}$ Thickness of bigger sphere $=\mathrm{t} / 4$ Mass of ice melted $=($ volume of sphere $) \times$ (density of ice) Let $\mathrm{K}_{1}$ and $\mathrm{K}_{2}$ be the thermal conductivities of larger and smaller sphere. 
<br/> <br/>For bigger sphere, $\frac{K_{1} 4 \pi(2 r)^{2} \times 100}{t / 4}=\frac{\frac{4}{3} \pi(2 r)^{3} \rho L}{25 \times 60}$
<br/> <br/>For smaller sphere,
<br/> <br/>$\frac{\mathrm{K}_{2} \times 4 \pi \mathrm{r}^{2} \times 100}{\mathrm{t}}=$  $\frac{\frac{4}{3} \pi(2 \mathrm{r})^{3} \rho \mathrm{L}}{25 \times 60}$</div>


tags: ['Chemistry', 'Chemical Kinetics', 'BITSAT', 'BITSAT 2014']
source_db: MarksBatch2_P3.db
title:
two-substances-r-and-s-decompose-in-solution-independently-both-following-first-order-kinetics-the-rate-constant-of-r-is-twice-that-of-s-in-an-experim

slug:
two-substances-r-and-s-decompose-in-solution-independently-both-following-first-order-kinetics-the-rate-constant-of-r-is-twice-that-of-s-in-an-experim-65885

question:
<div class="question">Two substances $\mathrm{R}$ and $\mathrm{S}$ decompose in solution independently, both following first order kinetics. The rate constant of $\mathrm{R}$ is twice that of $\mathrm{S}$. In an experiment, the solution initially contained 0.5 millimoles of $\mathrm{R}$ and 0.25 of $\mathrm{S}$. The molarities of $\mathrm{R}$ and $\mathrm{S}$ will be equal just at the end of time equal to</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">twice the half life of $\mathrm{R}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">twice the half life of $S$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">the half life of $\mathrm{S}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">the half life of $\mathrm{R}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">twice the half life of $\mathrm{R}$</span> </div>

answer:
<div class="solution">Substance $\mathrm{R}$ Substance $\mathrm{S}$ $2 \mathrm{k} \quad \mathrm{k}$ rate constant $\mathrm{t}_{1 / 2}=\mathrm{n} \times \mathrm{t}_{1 / 2}$
<br/> <br/>where $\mathrm{n}=$ number of half life period
<br/> <br/>Amount of $\mathrm{R}$ left $=\frac{0.5}{(2)^{\mathrm{T} / \mathrm{t}_{/ 2}}}$
<br/> <br/>Amount of $\mathrm{S}$ left $=\frac{0.25}{(2)^{\mathrm{T} / 2 \mathrm{t} / 2}}$
<br/> <br/>Equating both $\frac{0.5}{0.25}=\frac{(2)^{\mathrm{T} / \mathrm{t}_{1 / 2}}}{(2)^{\mathrm{T} / 2 \mathrm{t}_{1 / 2}}}$
<br/> <br/>or $2=(2)^{\mathrm{T} / \mathrm{t}_{1 / 2}}$
<br/> <br/>$\therefore \mathrm{T}=2 \mathrm{t}_{1 / 2} \cdot 2 \mathrm{t}_{1 / 2}$ is half life of $\mathrm{S}$ and
<br/> <br/>twice the half -life of $\mathrm{R}$</div>


tags: ['Mathematics', 'Limits', 'BITSAT', 'BITSAT 2009']
source_db: MarksBatch2_P3.db
title:
two-tangents-p-q-and-p-r-drawn-to-the-circle-x2y22-x4-y200-from-point-p167-ifthe-centre-of-the-circle-is-c-then-the-area-of-quadrilateral-mathrmpqcr-i

slug:
two-tangents-p-q-and-p-r-drawn-to-the-circle-x2y22-x4-y200-from-point-p167-ifthe-centre-of-the-circle-is-c-then-the-area-of-quadrilateral-mathrmpqcr-i-47032

question:
<div class="question">Two tangents \(P Q\) and \(P R\) drawn to the circle \(x^2+y^2-2 x-4 y-20=0\) from point \(P(16,7)\). Ifthe centre of the circle is \(C\) then the area of quadrilateral \(\mathrm{PQCR}\) is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">75 sq. unit</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">73 sq. unit</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">72 sq. unit</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">74 sq. unit</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">75 sq. unit</span> </div>

answer:
<div class="solution">Area \(\mathrm{PQCR}=2~ \triangle ~\mathrm{PQC}=2 \times \frac{1}{2} \mathrm{~L} \times r\)<br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/2MlwpK4A6CfMHiqk-ouZZSz-r8ZeW9skHwUpBdQRtt0.original.fullsize.png"/><br/><br/>where \(\mathrm{L}=\) length of tangent and \(r=\) radius of circle.<br/>\(\mathrm{L}=\sqrt{\mathrm{S}_1}=15 \text { and } \mathrm{r}=\sqrt{1+4+20}=5\)<br/>Hence the required area \(=75\) sq. units.</div>


tags: ['Physics', 'Waves and Sound', 'BITSAT', 'BITSAT 2009']
source_db: MarksBatch2_P3.db
title:
two-tuning-forks-a-and-b-sounded-together-give-6-beats-per-second-with-an-air-resonance-tube-closed-at-one-end-the-two-forks-give-resonance-when-the-t

slug:
two-tuning-forks-a-and-b-sounded-together-give-6-beats-per-second-with-an-air-resonance-tube-closed-at-one-end-the-two-forks-give-resonance-when-the-t-96473

question:
<div class="question">Two tuning forks $A$ and $B$ sounded together give 6 beats per second. With an air resonance tube closed at one end, the two forks give resonance when the two air columns are $24 \mathrm{~cm}$ and 25 $\mathrm{cm}$ respectively. Calculate the frequencies of forks.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$120 \mathrm{~Hz}, 124 \mathrm{~Hz}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$110 \mathrm{~Hz}, 114 \mathrm{~Hz}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$150 \mathrm{~Hz}, 144 \mathrm{~Hz}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$170 \mathrm{~Hz}, 118 \mathrm{~Hz}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$150 \mathrm{~Hz}, 144 \mathrm{~Hz}$</span> </div>

answer:
<div class="solution">Let the frequency of the first fork be $\mathrm{f}_{1}$ and that of second be $\mathrm{f}_{2}$<br/>We then have, $\mathrm{f}_{1}=\frac{\mathrm{v}}{4 \times 24}$ and $\mathrm{f}_{2}=\frac{\mathrm{v}}{4 \times 25}$<br/>We also see that $\mathrm{f}_{1}&gt;\mathrm{f}_{2}$<br/>$$<br/>\therefore \mathrm{f}_{1}-\mathrm{f}_{2}=6<br/>$$<br/>and $\frac{\mathrm{f}_{1}}{\mathrm{f}_{2}}=\frac{24}{25}$<br/>Solving (i) and (ii), we get $\mathrm{f}_{1}=150 \mathrm{~Hz}$ and $\quad \mathrm{f}_{2}=144 \mathrm{~Hz}$</div>


tags: ['Physics', 'Waves and Sound', 'BITSAT', 'BITSAT 2015']
source_db: MarksBatch2_P3.db
title:
two-tuning-forks-with-natural-frequencies-340-hz-each-move-relative-to-a-stationary-observer-one-fork-moves-away-from-the-observer-while-the-other-mov

slug:
two-tuning-forks-with-natural-frequencies-340-hz-each-move-relative-to-a-stationary-observer-one-fork-moves-away-from-the-observer-while-the-other-mov-39494

question:
<div class="question">Two tuning forks with natural frequencies 340 Hz each move relative to a stationary observer. One fork moves away from the observer, while the other moves towards the observer at the same speed. The observer hears beats offrequency $3 \mathrm{~Hz}$. Find the speed of the tuning forks.</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$1.5 \mathrm{~m} / \mathrm{s}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$2 \mathrm{~m} / \mathrm{s}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$1 \mathrm{~m} / \mathrm{s}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$2.5 \mathrm{~m} / \mathrm{s}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$1.5 \mathrm{~m} / \mathrm{s}$</span> </div>

answer:
<div class="solution">Let $v=$ speed of sound and $v_{\mathrm{S}}=$ speed of tuning forks. Apparent frequency of fork moving towards the observer is
<br/> <br/>$$
<br/> <br/>\mathrm{n}_{1}=\left(\frac{\mathrm{v}}{\mathrm{v}-\mathrm{v}_{\mathrm{s}}}\right) \mathrm{n}
<br/> <br/>$$
<br/> <br/>Apparent frequency of the fork moving away from the observer is
<br/> <br/>$$
<br/> <br/>\mathrm{n}_{2}=\left(\frac{\mathrm{v}}{\mathrm{v}+\mathrm{v}_{\mathrm{s}}}\right) \mathrm{n}
<br/> <br/>$$
<br/> <br/>If $f$ is the number of beats heard per second. then $\mathrm{f}=\mathrm{n}_{1}-\mathrm{n}_{2}$
<br/> <br/>$$
<br/> <br/>\begin{array}{l}
<br/> <br/>\Rightarrow \mathrm{f}=\left(\frac{\mathrm{v}}{\mathrm{v}-\mathrm{v}_{\mathrm{s}}}\right) \mathrm{n}-\left(\frac{\mathrm{v}}{\mathrm{v}+\mathrm{v}_{\mathrm{s}}}\right) \mathrm{n} \\
<br/> <br/>\Rightarrow \mathrm{f}=\frac{\mathrm{v}\left(\mathrm{v}+\mathrm{v}_{\mathrm{s}}\right)-\mathrm{v}\left(\mathrm{v}-\mathrm{v}_{\mathrm{s}}\right)}{\mathrm{v}^{2}-\mathrm{v}_{\mathrm{s}}^{2}}(\mathrm{n}) \\
<br/> <br/>\Rightarrow \frac{2 \mathrm{vv}_{\mathrm{s}} \mathrm{n}}{\mathrm{v}^{2}-\mathrm{v}_{\mathrm{s}}^{2}}=\mathrm{f} \Rightarrow 2\left(\frac{\mathrm{v}_{\mathrm{s}}}{\mathrm{v}}\right)=\mathrm{n}=\mathrm{f}\left\{\right.\text { if } \mathrm{v}_{\mathrm{s}}&lt;\mathrm{K}v
<br/> <br/>\end{array}
<br/> <br/>$$
<br/> <br/>$$
<br/> <br/>\Rightarrow v_{\mathrm{s}}=\frac{\mathrm{fv}}{2 \mathrm{n}}
<br/> <br/>$$
<br/> <br/>$$
<br/> <br/>\begin{array}{l}
<br/> <br/>\text { putting } \mathrm{v}=340 \mathrm{~m} / \mathrm{s}, \mathrm{f}=3, \mathrm{n}=340 \mathrm{~Hz} \text { we get, } \\
<br/> <br/>\mathrm{v}_{\mathrm{s}}=\frac{340 \times 3}{3 \times 340}=1.5 \mathrm{~m} / \mathrm{s}
<br/> <br/>\end{array}
<br/> <br/>$$</div>


tags: ['Mathematics', 'Vector Algebra', 'BITSAT', 'BITSAT 2011']
source_db: MarksBatch2_P3.db
title:
two-vectors-veca-and-vecb-are-such-that-overrightarrowmathrmaoverrightarrowmathrmboverrightarrowmathrmaoverrightarrowmathrmb-the-angle-between-the-two

slug:
two-vectors-veca-and-vecb-are-such-that-overrightarrowmathrmaoverrightarrowmathrmboverrightarrowmathrmaoverrightarrowmathrmb-the-angle-between-the-two-34992

question:
<div class="question">Two vectors \(\vec{A}\) and \(\vec{B}\) are such that \(|\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}|=|\overrightarrow{\mathrm{A}}-\overrightarrow{\mathrm{B}}|\). The angle between the two vectors will be-</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">\(60^{\circ}\)</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">\(90^{\circ}\)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">\(180^{\circ}\)</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">\(0^{\circ}\)</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\(90^{\circ}\)</span> </div>

answer:
<div class="solution">\(\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}|=| \overrightarrow{\mathrm{A}}-\overrightarrow{\mathrm{B}} \mid\)<br/>\(\Rightarrow \sqrt{\mathrm{A}^2+\mathrm{B}^2+2 \mathrm{AB} \cos \theta}=\sqrt{\mathrm{A}^2+\mathrm{B}^2-2 \mathrm{AB} \cos \theta}\)<br/>Squaring both the sides, we get<br/>\(\overrightarrow{\mathrm{A}}^2+\overrightarrow{\mathrm{B}}^2+2 \overrightarrow{\mathrm{A}} \overrightarrow{\mathrm{B}} \cos \theta=\overrightarrow{\mathrm{A}}^2+\overrightarrow{\mathrm{B}}^2-2 \overrightarrow{\mathrm{A}} \overrightarrow{\mathrm{B}} \cos \theta\)<br/>or \(4 \overrightarrow{\mathrm{A}} \overrightarrow{\mathrm{B}} \cos \theta=0\) or \(\cos \theta=0\) (since the scalar or dot product is zero). Therefore angle between \(\overrightarrow{\mathrm{A}}\) to \(\overrightarrow{\mathrm{B}}\) is \(90^{\circ}\)</div>


tags: ['Chemistry', 'States of Matter', 'BITSAT', 'BITSAT 2020']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">2</span> </div>
source_db: MarksBatch2_P3.db
title:
two-vessels-of-volumes-164-l-and-5-l-contain-two-ideal-gases-of-molecular-existence-at-the-respective-temperature-of-2-7-c-and-22-7-c-and-exert-15-and

slug:
two-vessels-of-volumes-164-l-and-5-l-contain-two-ideal-gases-of-molecular-existence-at-the-respective-temperature-of-2-7-c-and-22-7-c-and-exert-15-and-62416

question:
<div class="question">Two vessels of volumes $16.4 \mathrm{~L}$ and $5 \mathrm{~L}$ contain two ideal gases of molecular existence at the respective temperature of $27^{\circ} \mathrm{C}$ and $227^{\circ} \mathrm{C}$ and exert 1.5 and 4.1 atmospheres respectively. The ratio of the number of molecules of the former to that of the later is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">2</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">1</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{1}{2}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{1}{3}$</span> </li> </ul>

answer:
<div class="solution">Given conditions $\mathrm{V}_{1}=16.4 \mathrm{~L}, \mathrm{~V}_{2}=5 \mathrm{~L}$
<br/> <br/>$\mathrm{P}_{1}=1.5 \mathrm{~atm}, \mathrm{P}_{2}=4.1 \mathrm{~atm}$
<br/> <br/>$\mathrm{T}_{1}=273+27=300 \mathrm{~K}$
<br/> <br/>$\mathrm{T}_{2}=273+227=500 \mathrm{~K}$
<br/> <br/>Applying gas equation, $\frac{\mathrm{P}_{1} \mathrm{~V}_{1}}{\mathrm{P}_{2} \mathrm{~V}_{2}}=\frac{\mathrm{n}_{1} \mathrm{~T}_{1}}{\mathrm{n}_{2} \mathrm{~T}_{2}}$
<br/> <br/>$\frac{\mathrm{n}_{1}}{\mathrm{n}_{2}}=\frac{\mathrm{P}_{1} \mathrm{~V}_{1} \mathrm{~T}_{1}}{\mathrm{P}_{2} \mathrm{~V}_{2} \mathrm{~T}_{2}}$
<br/> <br/>$\therefore \frac{1.5 \times 16.4 \times 500}{4.1 \times 5 \times 300}=\frac{2}{1}$</div>


tags: ['Physics', 'Waves and Sound', 'BITSAT', 'BITSAT 2013']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">4</span> </div>
source_db: MarksBatch2_P3.db
title:
two-waves-of-wavelengths-99-cm-and-100-cm-both-travelling-with-velocity-396-m-s-are-made-to-interfere-the-number-of-beats-produced-by-them-per-second-

slug:
two-waves-of-wavelengths-99-cm-and-100-cm-both-travelling-with-velocity-396-m-s-are-made-to-interfere-the-number-of-beats-produced-by-them-per-second-23797

question:
<div class="question">Two waves of wavelengths $99 \mathrm{~cm}$ and $100 \mathrm{~cm}$ both travelling with velocity $396 \mathrm{~m} / \mathrm{s}$ are made to interfere. The number of beats produced by them per second is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">1</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">2</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">4</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">8</span> </li> </ul>

answer:
<div class="solution">Velocity of wave $\mathrm{v}=\mathrm{n} \lambda$ where $n=$ frequency of wave $\Rightarrow n=\frac{v}{\lambda}$
<br/> <br/>$\mathrm{n}_{2}=\frac{\mathrm{v}_{2}}{\lambda_{2}}=\frac{396}{100 \times 10^{-2}}=396 \mathrm{~Hz}$
<br/> <br/>no. of beats $=\mathrm{n}_{1}-\mathrm{n}_{2}=4$</div>


tags: ['Physics', 'Current Electricity', 'BITSAT', 'BITSAT 2020']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">16: 1</span> </div>
source_db: MarksBatch2_P3.db
title:
two-wires-a-and-b-of-the-same-material-having-radii-in-the-ratio-1-2-and-carry-currents-in-the-ratio-4-1-the-ratio-of-drift-speed-of-electrons-in-a-an

slug:
two-wires-a-and-b-of-the-same-material-having-radii-in-the-ratio-1-2-and-carry-currents-in-the-ratio-4-1-the-ratio-of-drift-speed-of-electrons-in-a-an-35632

question:
<div class="question">Two wires $\mathrm{A}$ and $\mathrm{B}$ of the same material, having radii in the ratio 1: 2 and carry currents in the ratio 4: 1 . The ratio of drift speed of electrons in $\mathrm{A}$ and $\mathrm{B}$ is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">16: 1</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">1: 16</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">1: 4</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">4: 1</span> </li> </ul>

answer:
<div class="solution">Current flowing through the conductor, $\mathrm{I}=\mathrm{n} \mathrm{e} \mathrm{v} \mathrm{A}$. Hence
<br/> <br/>$\frac{4}{1}=\frac{\text { nev }_{\mathrm{d}_{1}} \pi(1)^{2}}{\operatorname{nev}_{\mathrm{d}_{2}} \pi(2)^{2}}$ or $\frac{v_{\mathrm{d}_{1}}}{\mathrm{v}_{\mathrm{d}_{2}}}=\frac{4 \times 1}{1}=\frac{16}{1}$</div>


tags: ['Physics', 'Mechanical Properties of Solids', 'BITSAT', 'BITSAT 2016']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$9 F$</span> </div>
source_db: MarksBatch2_P3.db
title:
two-wires-are-made-of-the-same-material-and-have-the-same-volume-however-wire-1-has-crosssectional-area-a-and-wire-2-has-crosssectional-area-3-a-if-th-1

slug:
two-wires-are-made-of-the-same-material-and-have-the-same-volume-however-wire-1-has-crosssectional-area-a-and-wire-2-has-crosssectional-area-3-a-if-th-1-97864

question:
<div class="question">Two wires are made of the same material and have the same volume. However wire 1 has crosssectional area $A$ and wire 2 has cross-sectional area $3 A$. If the length of wire 1 increases by $\Delta x$ on applying force $F$, how much force is needed to stretch wire 2 by the same amount?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$4 F$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$6 \mathrm{~F}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$9 F$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$F$</span> </li> </ul>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/P0k_WTvgv0rpNlNioPi2bv36mXT2k6sjpIj_hQkJ47w.original.fullsize.png"/><br/> <br/> <br/>As shown in the figure, the wires will have the same Young's modulus (same material) and the length of the wire of area of crosssection $3 A$ will be $\ell / 3$ (same volume as wire 1 ). For wire $1, \quad Y=\frac{F / A}{\Delta x / \ell}$
<br/> <br/>For wire $2, Y=\frac{F^{\prime} / 3 A}{\Delta x /(\ell / 3)}$
<br/> <br/>From (i) and
<br/> <br/>(ii) $, \frac{F}{A} \times \frac{\ell}{\Delta x}=\frac{F^{\prime}}{3 A} \times \frac{\ell}{3 \Delta x}$
<br/> <br/>$\Rightarrow F^{\prime}=9 F$</div>


tags: ['Physics', 'Mechanical Properties of Solids', 'JEE Main']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$9 F$</span> </div>
source_db: MarksBatch2_P3.db
title:
two-wires-are-made-of-the-same-material-and-have-the-same-volume-however-wire-1-has-crosssectional-area-a-and-wire-2-has-crosssectional-area-3-a-if-th-2

slug:
two-wires-are-made-of-the-same-material-and-have-the-same-volume-however-wire-1-has-crosssectional-area-a-and-wire-2-has-crosssectional-area-3-a-if-th-2-99778

question:
<div class="question">Two wires are made of the same material and have the same volume. However wire 1 has crosssectional area $A$ and wire 2 has cross-sectional area $3 A$. If the length of wire 1 increases by $\Delta x$ on applying force $F,$ how much force is needed to stretch wire 2 by the same amount?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$4 F$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$6 F$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$9 F$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$F$</span> </li> </ul>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/kk2F602ESmY8WuB4l4rk_KWl7o6VunDItj7oIZB1qpg.original.fullsize.png"/><br/><br/>As shown in the figure, the wires will have the same Young's modulus (same material) and the length of the wire of area of crosssection $3 A$ will be $\ell / 3$ (samevolume as wire 1 ). For wire $1, \quad Y=\frac{F / A}{\Delta x / \ell}$<br/>For wire $2, Y=\frac{F^{\prime} / 3 A}{\Delta x /(\ell / 3)}$<br/>From (i) and (ii) $, \frac{F}{A} \times \frac{\ell}{\Delta x}=\frac{F^{\prime}}{3 A} \times \frac{\ell}{3 \Delta x}$<br/>$\Rightarrow F^{\prime}=9 F$</div>


tags: ['Physics', 'Mechanical Properties of Solids', 'JEE Main']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$9 F$</span> </div>
source_db: MarksBatch2_P3.db
title:
two-wires-are-made-of-the-same-material-and-have-the-same-volume-however-wire-1-has-crosssectional-area-a-and-wire-2-has-crosssectional-area-3-a-if-th-3

slug:
two-wires-are-made-of-the-same-material-and-have-the-same-volume-however-wire-1-has-crosssectional-area-a-and-wire-2-has-crosssectional-area-3-a-if-th-3-22344

question:
<div class="question">Two wires are made of the same material and have the same volume. However wire 1 has crosssectional area $A$ and wire 2 has cross-sectional area $3 A$. If the length of wire 1 increases by $\Delta x$ on applying force $F$, how much force is needed to stretch wire 2 by the same amount?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$4 F$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$6 \mathrm{~F}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$9 F$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$F$</span> </li> </ul>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/P0k_WTvgv0rpNlNioPi2bv36mXT2k6sjpIj_hQkJ47w.original.fullsize.png"/><br/> <br/> <br/>As shown in the figure, the wires will have the same Young's modulus (same material) and the length of the wire of area of crosssection $3 A$ will be $\ell / 3$ (same volume as wire 1 ). For wire $1, \quad Y=\frac{F / A}{\Delta x / \ell}$
<br/> <br/>For wire $2, Y=\frac{F^{\prime} / 3 A}{\Delta x /(\ell / 3)}$
<br/> <br/>From (i) and
<br/> <br/>(ii) $, \frac{F}{A} \times \frac{\ell}{\Delta x}=\frac{F^{\prime}}{3 A} \times \frac{\ell}{3 \Delta x}$
<br/> <br/>$\Rightarrow F^{\prime}=9 F$</div>


tags: ['Physics', 'Mechanical Properties of Solids', 'BITSAT', 'BITSAT 2011']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$9 F$</span> </div>
source_db: MarksBatch2_P3.db
title:
two-wires-are-made-of-the-same-material-and-have-the-same-volume-however-wire-1-has-crosssectional-area-a-and-wire-2-has-crosssectional-area-3-a-if-th

slug:
two-wires-are-made-of-the-same-material-and-have-the-same-volume-however-wire-1-has-crosssectional-area-a-and-wire-2-has-crosssectional-area-3-a-if-th-40917

question:
<div class="question">Two wires are made of the same material and have the same volume. However wire 1 has crosssectional area $A$ and wire 2 has cross-sectional area $3 A$. If the length of wire 1 increases by $\Delta x$ on applying force $F,$ how much force is needed to stretch wire 2 by the same amount?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$4 F$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$6 F$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$9 F$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$F$</span> </li> </ul>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/kk2F602ESmY8WuB4l4rk_KWl7o6VunDItj7oIZB1qpg.original.fullsize.png"/><br/><br/>As shown in the figure, the wires will have the same Young's modulus (same material) and the length of the wire of area of crosssection $3 A$ will be $\ell / 3$ (samevolume as wire 1 ). For wire $1, \quad Y=\frac{F / A}{\Delta x / \ell}$<br/>For wire $2, Y=\frac{F^{\prime} / 3 A}{\Delta x /(\ell / 3)}$<br/>From (i) and (ii) $, \frac{F}{A} \times \frac{\ell}{\Delta x}=\frac{F^{\prime}}{3 A} \times \frac{\ell}{3 \Delta x}$<br/>$\Rightarrow F^{\prime}=9 F$</div>


tags: ['Chemistry', 'Chemical Kinetics', 'BITSAT', 'BITSAT 2018']
source_db: MarksBatch2_P3.db
title:
under-the-same-reaction-conditions-initial-concentration-of-1-386-mol-dm-3-of-a-substance-becomes-half-in-40-s-and-20-s-through-first-order-and-zero-o

slug:
under-the-same-reaction-conditions-initial-concentration-of-1-386-mol-dm-3-of-a-substance-becomes-half-in-40-s-and-20-s-through-first-order-and-zero-o-49426

question:
<div class="question">Under the same reaction conditions, initial concentration of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>386</mn><mo> </mo><mi>mol</mi><mo> </mo><msup><mi>dm</mi><mrow><mo>-</mo><mn>3</mn></mrow></msup></math> of a substance becomes half in <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>40</mn><mo> </mo><mi mathvariant="normal">s</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo> </mo><mi mathvariant="normal">s</mi></math> through first order and zero order kinetics, respectively. Ratio <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mfrac><msub><mi mathvariant="normal">k</mi><mn>1</mn></msub><msub><mi mathvariant="normal">k</mi><mn>0</mn></msub></mfrac></mfenced></math> of the rate of constants for first order <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><msub><mi mathvariant="normal">k</mi><mn>1</mn></msub></mfenced></math> and zero order <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><msub><mi mathvariant="normal">k</mi><mn>0</mn></msub></mfenced></math> of the reaction is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>5</mn><mo> </mo><msup><mi>mol</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><msup><mi>dm</mi><mn>3</mn></msup></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>0</mn><mo> </mo><mi>mol</mi><mo> </mo><msup><mi>dm</mi><mrow><mo>-</mo><mn>3</mn></mrow></msup></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>5</mn><mo> </mo><msup><mi>moldm</mi><mrow><mo>-</mo><mn>3</mn></mrow></msup></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>0</mn><mo> </mo><msup><mi>mol</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><msup><mi>dm</mi><mn>3</mn></msup></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>5</mn><mo> </mo><msup><mi>mol</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><msup><mi>dm</mi><mn>3</mn></msup></math></span> </div>

answer:
<div class="solution"><p>Given that, </p><p>Under the same reaction conditions, initial concentration of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>386</mn><mo> </mo><mi>mol</mi><mo> </mo><msup><mi>dm</mi><mrow><mo>-</mo><mn>3</mn></mrow></msup></math> of a substance becomes half in <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>40</mn><mo> </mo><mi mathvariant="normal">s</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo> </mo><mi mathvariant="normal">s</mi></math>for first order and zero order kinetics, respectively.</p><p>For first order reaction,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">t</mi><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msub><mo>=</mo><mfrac><mrow><mi>ln</mi><mn>2</mn></mrow><msub><mi mathvariant="normal">k</mi><mn>1</mn></msub></mfrac><mo>=</mo><mn>40</mn><mo> </mo><mi mathvariant="normal">s</mi><mo>.</mo><mo>.</mo><mo>.</mo><mfenced><mi mathvariant="normal">i</mi></mfenced></math></p><p>For zero order reaction, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">t</mi><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msub><mo>=</mo><mfrac><msub><mfenced close="]" open="["><mi mathvariant="normal">A</mi></mfenced><mn>0</mn></msub><mrow><mn>2</mn><msub><mi mathvariant="normal">k</mi><mn>0</mn></msub></mrow></mfrac><mo>=</mo><mn>20</mn><mo> </mo><mi mathvariant="normal">s</mi><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><mfenced><mi>ii</mi></mfenced></math></p><p>Divide eqn. (i) by (ii), we get</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>=</mo><mfrac><mrow><mo>[</mo><mi mathvariant="normal">A</mi><msub><mo>]</mo><mn>0</mn></msub></mrow><mrow><mn>2</mn><msub><mi mathvariant="normal">k</mi><mn>0</mn></msub></mrow></mfrac><mo>×</mo><mfrac><msub><mi mathvariant="normal">k</mi><mn>1</mn></msub><mrow><mi>ln</mi><mn>2</mn></mrow></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msub><mi mathvariant="normal">k</mi><mn>1</mn></msub><msub><mi mathvariant="normal">k</mi><mn>0</mn></msub></mfrac><mo>=</mo><mfrac><mrow><mi>ln</mi><mn>2</mn></mrow><mrow><mo>[</mo><mi mathvariant="normal">A</mi><msub><mo>]</mo><mn>0</mn></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>0</mn><mo>.</mo><mn>693</mn></mrow><mrow><mn>1</mn><mo>.</mo><mn>386</mn></mrow></mfrac><mo>=</mo><mn>0</mn><mo>.</mo><mn>5</mn><mo> </mo><msup><mi>mol</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><msup><mi>dm</mi><mn>3</mn></msup></math> </p></div>


title: universal-set-u-x-x-5-6-x-4-11-x-3-6-x-2-0-a-x-x-2-5-x-6-0-b-x-x-2-3-x-2-0-what-is-a-b-equal-to-1
tags: ['Mathematics', 'Sets and Relations', 'BITSAT', 'BITSAT 2015']
source_db: MarksBatch2_P3.db
slug:
universal-set-u-x-x-5-6-x-4-11-x-3-6-x-2-0-a-x-x-2-5-x-6-0-b-x-x-2-3-x-2-0-what-is-a-b-equal-to-1-47006

question:
<div class="question">Universal set,
<br/>$U=\left\{x \mid x^{5}-6 x^{4}+11 x^{3}-6 x^{2}=0\right\}$
<br/> $A=\left\{x \mid x^{2}-5 x+6=0\right\}$  $\mathrm{B}=\left\{\mathrm{x} \mid \mathrm{x}^{2}-3\mathrm{x}+2=0\right\}$
<br/> <br/>What is $(A \cap B)^{\prime}$ equal to ?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">{1,3}</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">{1,2,3}</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">{0,1,3}</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">{0,1,2,3}</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">{0,1,3}</span> </div>

answer:
<div class="solution">$U=\left\{x: x^{5}-6 x^{4}+11 x^{3}-6 x^{2}=0\right\}$
<br/> <br/>Solving for values of $x$, we get $\mathrm{U}=\{0,1,2,3\}$
<br/> <br/>$\mathrm{A}=\left\{\mathrm{x}: \mathrm{x}^{2}-5 \mathrm{x}+6=0\right\}$
<br/> <br/>Solving for values of $x$, we get $\mathrm{A}=\{2,3\}$
<br/> <br/>and $\mathrm{B}=\left\{\mathrm{x}: \mathrm{x}^{2}-3 \mathrm{x}+2=0\right\}$
<br/> <br/>Solving for values of $x$, we get $\mathrm{B}=\{2,1\}$
<br/> <br/>$A \cap B=\{2\}$
<br/> <br/>$\therefore(A \cap B)^{\prime}=U-(A \cap B)$
<br/> <br/>$=\{0,1,2,3\}-\{2\}=\{0,1,3\}$</div>


title: using-mot-which-of-the-following-pairs-denote-paramagnetic-species
slug: using-mot-which-of-the-following-pairs-denote-paramagnetic-species-97602
question: <div class="question">Using MOT, which of the following pairs denote paramagnetic species?</div>
tags: ['Chemistry', 'Chemical Bonding and Molecular Structure', 'BITSAT', 'BITSAT 2013']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{B}_{2}$ and $\mathrm{C}_{2}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\mathrm{B}_{2}$ and $\mathrm{O}_{2}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{N}_{2}$ and $\mathrm{C}_{2}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{O}_{2}$ and $\mathrm{O}_{2}^{2-}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{B}_{2}$ and $\mathrm{O}_{2}$</span> </div>

answer:
<div class="solution">$\mathrm{B}_{2}$ and $\mathrm{O}_{2}$ are paramagnetic due to presence of unpaired electron. MO electronic configuration of $\mathrm{B}_{2}$ is:
<br/> <br/>$$
<br/> <br/>\sigma 1 s^{2} \sigma^{*} 1 s^{2} \sigma 2 s^{2} \sigma^{*} 2 s^{2} \pi 2 p_{x}^{1}=\pi 2 p_{y}^{1}
<br/> <br/>$$
<br/> <br/>MO electorn i.e. configuration of $\mathrm{O}_{2}$ is:
<br/> <br/>$$
<br/> <br/>\begin{array}{l}
<br/> <br/>\sigma 1 s^{2} \sigma^{*} 1 s^{2} \sigma 2 s^{2} \sigma^{*} 2 s^{2} \sigma 2 p_{z}^{2} \pi 2 p_{x}^{2} \\
<br/> <br/>=\pi 2 p_{y}^{2} \pi * 2 p_{x}^{1}=\pi * 2 p_{y}^{1}
<br/> <br/>\end{array}
<br/> <br/>$$</div>


tags: ['Chemistry', 'Electrochemistry', 'BITSAT', 'BITSAT 2022']
source_db: MarksBatch2_P3.db
title:
using-the-standard-electrode-potential-find-out-the-pair-between-which-redox-reaction-is-not-feasible-e-values-fe-3-fe-2-077-i-2-i-054-cu-2-cu-034-ag-

slug:
using-the-standard-electrode-potential-find-out-the-pair-between-which-redox-reaction-is-not-feasible-e-values-fe-3-fe-2-077-i-2-i-054-cu-2-cu-034-ag-26545

question:
<div class="question">Using the standard electrode potential, find out the pair between which redox reaction is not feasible.
<br/>$E^{\ominus}$ values $\mathrm{Fe}^{3+} / \mathrm{Fe}^{2+}=+0.77 ; \mathrm{I}_2 / \mathrm{I}^{-}=+054$
<br/>$\mathrm{Cu}^{2+} / \mathrm{Cu}=+0.34 ; \mathrm{Ag}^{+} / \mathrm{Ag}=0.80 \mathrm{~V}$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"> <br/>$\mathrm{Fe}^{3+}$ and $\mathrm{I}^{-}$
<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"> <br/>$\mathrm{Ag}^{+}$and $\mathrm{Cu}$
<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"> <br/>$\mathrm{Fe}^{3+}$ and $\mathrm{Cu}$
<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"> <br/>Ag and $\mathrm{Fe}^{3+}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"> <br/>Ag and $\mathrm{Fe}^{3+}$</span> </div>

answer:
<div class="solution">(a)<img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/ok9PLwHyacfw60Pt-I1fhACQVQEJN7EEy9JanOILEpI.original.fullsize.png"/><br/> <br/>This reaction is feasible, since $E_{\text {cell }}^{\circ}$ is positive.
<br/>(b)<img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/nxJ1g2C_J4IFowzBWqJ3kIIwXxWO4-mowicPksj5AwY.original.fullsize.png"/><br/> <br/>This reaction is feasible, since $E_{\text {cell }}^{\circ}$ is positive.
<br/>(c)<img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/uYAzWqaCsCn9jugCPjGq85iTRaQXj2wyeTS2MRGdGo0.original.fullsize.png"/><br/> <br/>This reaction is feasible, since $E_{\text {cell }}^{\circ}$ is positive.
<br/>(d)<img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/rKlHBm3z2AO5UoILkXmMsxRAlIDwTgutH1XzMA8lvbQ.original.fullsize.png"/><br/> <br/>This reaction is not feasible, since $E_{\text {cell }}^{\circ}$ is negative.</div>


tags: ['Chemistry', 'Chemical Bonding and Molecular Structure', 'BITSAT', 'BITSAT 2018']
source_db: MarksBatch2_P3.db
title:
valence-electrons-in-the-element-a-are-3-and-that-in-element-b-are-6-most-probable-compound-formed-from-a-and-b-is

slug:
valence-electrons-in-the-element-a-are-3-and-that-in-element-b-are-6-most-probable-compound-formed-from-a-and-b-is-89680

question:
<div class="question">Valence electrons in the element <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">A</mi></math> are <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math> and that in element <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">B</mi></math> are <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math>. Most probable compound formed from <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">A</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">B</mi></math> is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">A</mi><mn>2</mn></msub><mi mathvariant="normal">B</mi></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>AB</mi><mn>2</mn></msub></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">A</mi><mn>6</mn></msub><msub><mi mathvariant="normal">B</mi><mn>3</mn></msub></math></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">A</mi><mn>2</mn></msub><msub><mi mathvariant="normal">B</mi><mn>3</mn></msub></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">A</mi><mn>2</mn></msub><msub><mi mathvariant="normal">B</mi><mn>3</mn></msub></math></span> </div>

answer:
<div class="solution"><p>Valence electrons in <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">A</mi><mo>=</mo><mn>3</mn></math></p><p>Valence electron in <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">B</mi><mo>=</mo><mn>6</mn></math></p><p>Thus, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">A</mi></math> is electropositive and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">B</mi></math> is electronegative, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">A</mi></math> can lose three electrons and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">B</mi></math> can gain two electrons to attain stable configuration.</p><p>Hence, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">A</mi></math> exist as <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi mathvariant="normal">A</mi><mrow><mn>3</mn><mo>+</mo></mrow></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">B</mi></math> as <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi mathvariant="normal">B</mi><mrow><mn>2</mn><mo>-</mo></mrow></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> Compound formed is <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">A</mi><mn>2</mn></msub><msub><mi mathvariant="normal">B</mi><mn>3</mn></msub></math></p></div>


title: value-of-lim-x-0-s-i-n-x-a-s-i-n-x-1-is
slug: value-of-lim-x-0-s-i-n-x-a-s-i-n-x-1-is-88052
question: <div class="question">Value of $\lim _{x \rightarrow 0} \frac{a^{\sin x}-1}{\sin x}$ is</div>
tags: ['Mathematics', 'Limits', 'BITSAT', 'BITSAT 2021']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\log \mathrm{a}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\sin x$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\log (\sin x)$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\cos x$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\log \mathrm{a}$</span> </div>

answer:
<div class="solution">We have, $\lim _{x \rightarrow 0} \frac{a^{\sin x}-1}{\sin x}=\lim _{y \rightarrow 0} \frac{a^{y}-1}{y}$ $=\log \mathrm{a}$, where $\mathrm{y}=\sin \mathrm{x}$
<br/> <br/>$\because \mathrm{x} \rightarrow 0 \Rightarrow \mathrm{y}=\sin \mathrm{x} \rightarrow 0$</div>


title: value-of-x-a-x-d-x-is
slug: value-of-x-a-x-d-x-is-76264
question: <div class="question">Value of $\int \frac{d x}{\sqrt{x(a-x)}}$ is</div>
tags: ['Mathematics', 'Indefinite Integration', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 2)']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$2 \sin ^{-1} \sqrt{\frac{x}{a}}+c$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$-2 \sin ^{-1} \sqrt{\frac{x}{a}}+c$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$2 \sin ^{-1} \frac{\sqrt{x}}{a}+c$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>None of these</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$2 \sin ^{-1} \sqrt{\frac{x}{a}}+c$</span> </div>

answer:
<div class="solution">Let $\mathrm{x}=\mathrm{a} \sin ^2 \theta$<br/>then $d x=2 a \sin \theta \cos \theta d \theta$<br/>$\begin{aligned}<br/>\therefore \quad I &amp; =\int \frac{2 a \sin \theta \cdot \cos \theta}{\sqrt{a \sin ^2 \theta \cdot a \cos ^2 \theta}} d \theta \\<br/>&amp; =2 \int d \theta=2 \theta+c \\<br/>&amp; =2 \sin ^{-1}(\sqrt{x / a})+c<br/>\end{aligned}$</div>


title: velocity-constant-of-a-reaction-at-290-k-was-found-to-be-32-1-0-3-at-300-k-it-will-be
slug: velocity-constant-of-a-reaction-at-290-k-was-found-to-be-32-1-0-3-at-300-k-it-will-be-33531
tags: ['Chemistry', 'Chemical Kinetics', 'BITSAT', 'BITSAT 2013']
source_db: MarksBatch2_P3.db
question:
<div class="question">Velocity constant of a reaction at $290 \mathrm{~K}$ was found to be $3.2 \times 10^{-3}$. At $300 \mathrm{~K}$ it will be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$1.28 \times 10^{-2}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$9.6 \times 10^{-3}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$6.4 \times 10^{-3}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$3.2 \times 10^{-4}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$6.4 \times 10^{-3}$</span> </div>

answer:
<div class="solution">The velocity constant doubles for every $10^{\circ} \mathrm{C}$ rise in temperature.</div>


tags: ['Physics', 'Oscillations', 'BITSAT', 'BITSAT 2015']
source_db: MarksBatch2_P3.db
title:
vertical-displacement-of-a-plank-with-a-body-of-mass-m-on-it-is-varying-according-to-law-ysin-omega-tsqrt3-cos-omega-t-the-minimum-value-of-omega-for-

slug:
vertical-displacement-of-a-plank-with-a-body-of-mass-m-on-it-is-varying-according-to-law-ysin-omega-tsqrt3-cos-omega-t-the-minimum-value-of-omega-for-14967

question:
<div class="question">Vertical displacement of a plank with a body of mass \(m\) on it is varying according to law \(y=\sin \omega t+\sqrt{3} \cos \omega t\). The minimum value of \(\omega\) for which the mass just breaks off the plank and the moment it occurs first after \(\mathrm{t}=0\), are given by</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">\(\sqrt{\mathrm{g} / 2}, \frac{\sqrt{2}}{6} \frac{\pi}{\sqrt{\mathrm{g}}}\)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">\(\frac{\mathrm{g}}{\sqrt{2}}, \frac{2}{3} \sqrt{\pi / \mathrm{g}}\)</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">\(\sqrt{\mathrm{g} / 2}, \frac{\pi}{3} \sqrt{2 / \mathrm{g}}\)</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">\(\sqrt{2 g}, \sqrt{2 \pi / 3 g}\)</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\(\sqrt{\mathrm{g} / 2}, \frac{\sqrt{2}}{6} \frac{\pi}{\sqrt{\mathrm{g}}}\)</span> </div>

answer:
<div class="solution">From, figure,
<br/> <br/>$$
<br/> <br/>\begin{array}{ll} 
<br/> <br/>&amp; \Lambda_{\mathrm{R}}=\sqrt{(\sqrt{3})^{2}+(1)^{2}}-2 \\
<br/> <br/>&amp; \theta=\tan ^{-1}\left(\frac{\sqrt{3}}{1}\right)=\frac{\pi}{3} \\
<br/> <br/>\therefore \quad &amp; \mathrm{y}=2 \sin \left(\omega \mathrm{t}+\frac{\pi}{3}\right)
<br/> <br/>\end{array}
<br/> <br/>$$
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/qDQXfpTAafdxXjRT0KmftJ2IGzUtwLnnUJibSYxYCl4.original.fullsize.png"/><br/> <br/> <br/>$$
<br/> <br/>\frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{dt}^{2}}=\mathrm{a}=-2 \omega^{2} \sin \left(\omega \mathrm{t}+\frac{\pi}{3}\right)
<br/> <br/>$$
<br/> <br/>$a_{\max }=-2 \omega^{2}=g$
<br/> <br/>For which mass just breaks off the plank $\omega=\sqrt{\mathrm{g} / 2}$
<br/> <br/>This will be happen for the first time when
<br/> <br/>$$
<br/> <br/>\begin{array}{l}
<br/> <br/>\omega \mathrm{t}+\frac{\pi}{3}+\frac{\pi}{2} \text { or } \omega \mathrm{t}=\frac{\pi}{6} \\
<br/> <br/>\therefore \quad \mathrm{t}=\frac{\pi}{6 \omega}=\frac{\pi}{6} \sqrt{\frac{2}{\mathrm{~g}}}
<br/> <br/>\end{array}
<br/> <br/>$$</div>


title: viscosity-is-the-property-of-a-liquid-due-to-which-it
slug: viscosity-is-the-property-of-a-liquid-due-to-which-it-14119
question: <div class="question">Viscosity is the property of a liquid due to which it :</div>
tags: ['Physics', 'Mechanical Properties of Fluids', 'BITSAT', 'BITSAT 2011']
answer: <div class="solution">No Solution available</div>
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">occupies minimum surface area</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">opposes relative motion between its adjacent layers</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">becomes spherical in shape</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">tends to regain its deformed position</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">opposes relative motion between its adjacent layers</span> </div>


tags: ['Physics', 'Alternating Current', 'BITSAT', 'BITSAT 2014']
source_db: MarksBatch2_P3.db
title:
voltage-v-and-current-i-in-a-c-circuit-are-given-by-v-50-sin-50-t-volt-i-50-sin-50-t-3-ma-the-power-dissipated-in-the-circuit-is

slug:
voltage-v-and-current-i-in-a-c-circuit-are-given-by-v-50-sin-50-t-volt-i-50-sin-50-t-3-ma-the-power-dissipated-in-the-circuit-is-51248

question:
<div class="question">Voltage $V$ and current $i$ in $A C$ circuit are given by $\mathrm{V}=50 \sin (50 \mathrm{t})$ volt, $\mathrm{i}=50 \sin \left(50 \mathrm{t}+\frac{\pi}{3}\right) \mathrm{mA}$
<br/> <br/>The power dissipated in the circuit is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$5.0 \mathrm{~W}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$2.5 \mathrm{~W}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$1.25 \mathrm{~W}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">zero</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$1.25 \mathrm{~W}$</span> </div>

answer:
<div class="solution">Given $V=50 \sin (50$ t) $V$ Maximum voltage, $\mathrm{V}_{0}=50 \mathrm{~V}$
<br/> <br/>$$
<br/> <br/>i=\left(50 t+\frac{\pi}{3}\right) \mathrm{mA}
<br/> <br/>$$
<br/> <br/>Maximum current, $i_{0}=50 \mathrm{~mA}=50 \times 10^{-3} \mathrm{~A}$
<br/> <br/>Power dissipated, $\mathrm{P}=\frac{\mathrm{i}_{0}}{\sqrt{2}} \times \frac{\mathrm{V}_{0}}{\sqrt{2}}$
<br/> <br/>$=\frac{50 \times 50 \times 10^{-3}}{2}=\frac{2500 \times 10^{-3}}{2}=1.25 \mathrm{~W}$</div>


title: volume-of-3-solution-of-sodium-carbonate-necessary-to-neutralise-a-litre-of-01-n-sulphuric-acid
tags: ['Chemistry', 'Redox Reactions', 'BITSAT', 'BITSAT 2013']
source_db: MarksBatch2_P3.db
slug:
volume-of-3-solution-of-sodium-carbonate-necessary-to-neutralise-a-litre-of-01-n-sulphuric-acid-72415

question:
<div class="question">Volume of $3 \%$ solution of sodium carbonate necessary to neutralise a litre of $0.1 \mathrm{~N}$ sulphuric acid</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$176.66 \mathrm{ml}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$156.6 \mathrm{ml}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$116.0 \mathrm{ml}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$196.1 \mathrm{ml}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$176.66 \mathrm{ml}$</span> </div>

answer:
<div class="solution">Normality of $3 \% \mathrm{Na}_{2} \mathrm{CO}_{3}$
<br/> <br/>$\mathrm{N}=\frac{3 \times 1000}{53 \times 100}=0.566 \mathrm{~N}$
<br/> <br/>For $\mathrm{H}_{2} \mathrm{SO}_{4}$ sol. $\mathrm{N}_{1}=0.1, \mathrm{~V}_{1}=100 \mathrm{~mL}$
<br/> <br/>For $\mathrm{Na}_{2} \mathrm{CO}_{3}$ sol. $\mathrm{N}_{2}=0.566$
<br/> <br/>Now apply $\mathrm{N}_{1} \mathrm{~V}_{1}=\mathrm{N}_{2} \mathrm{~V}_{2}$
<br/> <br/>$\mathrm{V}_{2}=\frac{\mathrm{N}_{1} \mathrm{~V}_{1}}{\mathrm{~N}_{2}}=\frac{0.1 \times 1000 \mathrm{~mL}}{0.566}=176.66 \mathrm{~mL}$</div>


tags: ['Physics', 'Mechanical Properties of Fluids', 'BITSAT', 'BITSAT 2015']
source_db: MarksBatch2_P3.db
title:
water-is-flowing-on-a-horizontal-fixed-surface-such-that-its-flow-velocity-varies-with-y-vertical-direction-as-v-k-a-2-2-y-2-a-3-y-3-if-coefficient-of

slug:
water-is-flowing-on-a-horizontal-fixed-surface-such-that-its-flow-velocity-varies-with-y-vertical-direction-as-v-k-a-2-2-y-2-a-3-y-3-if-coefficient-of-68412

question:
<div class="question">Water is flowing on a horizontal fixed surface, such that its flow velocity varies with $y$ (vertical direction) as $v=k\left(\frac{2 y^{2}}{a^{2}}-\frac{y^{3}}{a^{3}}\right) .$ If coefficient of viscosity for water is $\eta$, what will be shear stress between layers of water at $y=a$.</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{\eta k}{a}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{\eta}{k a}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{\eta a}{k}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of these</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{\eta k}{a}$</span> </div>

answer:
<div class="solution">Newton's law of viscosity, $F=\eta A \frac{d v}{d y}$
<br/> <br/>$$
<br/> <br/>\begin{array}{l}
<br/> <br/>\text { Stress }=\frac{F}{A}=\eta\left(\frac{d v}{d y}\right)=\eta k\left(\frac{4 y}{a^{2}}-\frac{3 y^{2}}{a^{3}}\right) \\
<br/> <br/>\text { At } y=a, \text { stress }=\eta k\left(\frac{4}{a}-\frac{3}{a}\right)=\frac{\eta k}{a}
<br/> <br/>\end{array}
<br/> <br/>$$</div>


tags: ['Physics', 'Units and Dimensions', 'BITSAT', 'BITSAT 2013']
source_db: MarksBatch2_P3.db
title:
wave-pulse-can-travel-along-a-tense-string-like-a-violin-spring-aseries-of-experiments-showed-that-the-wave-velocity-v-of-a-pulse-depends-on-the-follo

slug:
wave-pulse-can-travel-along-a-tense-string-like-a-violin-spring-aseries-of-experiments-showed-that-the-wave-velocity-v-of-a-pulse-depends-on-the-follo-55916

question:
<div class="question">Wave pulse can travel along a tense string like a violin spring. Aseries of experiments showed that the wave velocity $\mathrm{V}$ of a pulse depends on the following quantities, the tension T of the string, the cross-section area A of the string and then as per unit volume $\rho$ of the string. Obtain an expression for $V$ in terms of the $\mathrm{T}, \mathrm{A}$ and $\rho$ using dimensional analysis.</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\mathrm{V}=\mathrm{k} \sqrt{\frac{\mathrm{T}}{\mathrm{A} \rho}}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{V}=\mathrm{k} \sqrt{\frac{\mathrm{T}}{\mathrm{A}}}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$V=k \sqrt{\frac{A \rho}{T}}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of these</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{V}=\mathrm{k} \sqrt{\frac{\mathrm{T}}{\mathrm{A} \rho}}$</span> </div>

answer:
<div class="solution">Let $\mathrm{V}=\mathrm{kT}^{\mathrm{a}} \mathrm{A}^{\mathrm{b}} \rho^{\mathrm{c}}$,
<br/> <br/>$\mathrm{k}=$ dimensional constant
<br/> <br/>Writing dimension on both we side
<br/> <br/>$$
<br/> <br/>\begin{aligned}
<br/> <br/>\left[\mathrm{LT}^{-1}\right] &amp;=\left[\mathrm{MLT}^{-2}\right]^{a}\left[\mathrm{~L}^{2}\right]^{\mathrm{b}}\left[\mathrm{ML}^{-3}\right]^{\mathrm{c}} \\
<br/> <br/>&amp;=\left[\mathrm{M}^{\mathrm{a}+\mathrm{c}} \mathrm{L}^{\mathrm{a}+2 \mathrm{~b}-3 \mathrm{c}} \mathrm{T}^{-2 \mathrm{a}}\right]
<br/> <br/>\end{aligned}
<br/> <br/>$$
<br/> <br/>Comparing power on both sides we have
<br/> <br/>$$
<br/> <br/>\begin{array}{l}
<br/> <br/>a+c=0, a+2 b-3 c=1, \quad-2 a=-1 \\
<br/> <br/>\therefore \quad a=\frac{1}{2}, c=-\frac{1}{2} \Rightarrow b=-\frac{1}{2} \therefore V=k \sqrt{\frac{T}{A \rho}}
<br/> <br/>\end{array}
<br/> <br/>$$</div>


title: what-is-nh-4-in-a-solution-that-is-002-m-nh-3-001-m-koh-k-b-nh-3-18-1-0-5
slug: what-is-nh-4-in-a-solution-that-is-002-m-nh-3-001-m-koh-k-b-nh-3-18-1-0-5-40726
tags: ['Chemistry', 'Ionic Equilibrium', 'BITSAT', 'BITSAT 2022']
source_db: MarksBatch2_P3.db
question:
<div class="question">What is $\left[\mathrm{NH}_4^{+}\right]$in a solution that is $0.02 \mathrm{M} \mathrm{NH}_3$ $0.01 \mathrm{M} \mathrm{KOH} ?\left[K_b\left(\mathrm{NH}_3\right)=1.8 \times 10^{-5}\right]$</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"> <br/>$3.6 \times 10^{-5} \mathrm{M}$
<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"> <br/>$1.8 \times 10^{-5} \mathrm{M}$
<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"> <br/>$0.9 \times 10^{-5} \mathrm{M}$
<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"> <br/>$7.2 \times 10^{-5} \mathrm{M}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"> <br/>$3.6 \times 10^{-5} \mathrm{M}$
<br/></span> </div>

answer:
<div class="solution">$\mathrm{NH}_4 \mathrm{OH} \rightleftharpoons \mathrm{NH}_4^{+}+\mathrm{OH}^{-}$
<br/>$K_b=\frac{\left[\mathrm{NH}_4^{+}\right]\left[\mathrm{OH}^{-}\right]}{\left[\mathrm{NH}_4 \mathrm{OH}\right]}$
<br/>$1.8 \times 10^{-5}=\frac{\left[\mathrm{NH}_4^{+}\right][0.01]}{[0.02]}$
<br/>$\therefore \quad\left[\mathrm{NH}_4^{+}\right]=3.6 \times 10^{-5} \mathrm{M}$</div>


title: what-is-the-angle-between-the-two-straight-lines-y-2-3-x-5-and-y-2-3-x-7-2
slug: what-is-the-angle-between-the-two-straight-lines-y-2-3-x-5-and-y-2-3-x-7-2-22020
tags: ['Mathematics', 'Straight Lines', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 1)']
source_db: MarksBatch2_P3.db
question:
<div class="question">What is the angle between the two straight lines $y=(2-\sqrt{3}) x+5$ and $y=(2+\sqrt{3}) x-7 ?$</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$60^{\circ}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$45^{\circ}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$30^{\circ}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$15^{\circ}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$60^{\circ}$</span> </div>

answer:
<div class="solution">The given lines are:<br/>$y=(2-\sqrt{3}) x+5 \text { and } y=(2+\sqrt{3}) x-7$<br/>Therefore, slope of first line $=m_1=2-\sqrt{3}$ and slope of second line $=m_2=2+\sqrt{3}$<br/>$\therefore \quad \tan \theta=\left|\frac{m_2-m_1}{1+m_1 m_2}\right|=\left|\frac{2+\sqrt{3}-2+\sqrt{3}}{1+(4-3)}\right|$<br/>$=\left|\frac{2 \sqrt{3}}{2}\right|=\sqrt{3}=\tan \frac{\pi}{3} \Rightarrow \theta=\frac{\pi}{3}=60^{\circ}$</div>


title: what-is-the-area-bounded-by-ytan-x-y0-and-xfracpi4
slug: what-is-the-area-bounded-by-ytan-x-y0-and-xfracpi4-80010
question: <div class="question">What is the area bounded by \(y=\tan x, y=0\) and \(x=\frac{\pi}{4} ?\)</div>
tags: ['Mathematics', 'Area Under Curves', 'BITSAT', 'BITSAT 2011']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">\(\ell n ~2~ \mathrm{sq}\). units</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">\(\frac{\ell n 2}{2} ~\mathrm{sq}\). units</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">\(2~(\ell n ~2)~ \mathrm{sq}\). units</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of these</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\(\frac{\ell n 2}{2} ~\mathrm{sq}\). units</span> </div>

answer:
<div class="solution">Required area \(=\int_0^{\frac{\pi}{4}} \tan x d x\)<br/>\(=\ln |\sec 1|_0^{\frac{\pi}{4}}=\ln \sqrt{2}=\frac{\ln 2}{2}\)</div>


title: what-is-the-correct-increasing-order-of-bronsted-bases
slug: what-is-the-correct-increasing-order-of-bronsted-bases-77461
question: <div class="question">What is the correct increasing order of Bronsted bases?</div>
tags: ['Chemistry', 'Ionic Equilibrium', 'BITSAT', 'BITSAT 2015']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\mathrm{ClO}_{4}^{-}&lt;\mathrm{ClO}_{3}^{-}&lt;\mathrm{ClO}_{2}^{-}&lt;\mathrm{ClO}^{-}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{ClO}_{4}^{-}&gt;\mathrm{ClO}_{3}^{-}&gt;\mathrm{ClO}_{2}^{-}&gt;\mathrm{ClO}^{-}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{ClO}_{3}^{-}&lt;\mathrm{ClO}_{4}^{-}&lt;\mathrm{ClO}_{2}^{-}&lt;\mathrm{ClO}^{-}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{ClO}^{-}&gt;\mathrm{ClO}_{3}^{-}&gt;\mathrm{ClO}_{2}^{-}&lt;\mathrm{ClO}_{4}^{-}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{ClO}_{4}^{-}&lt;\mathrm{ClO}_{3}^{-}&lt;\mathrm{ClO}_{2}^{-}&lt;\mathrm{ClO}^{-}$</span> </div>

answer:
<div class="solution">$\mathrm{ClO}_{4}^{-}&lt;\mathrm{ClO}_{3}^{-}&lt;\mathrm{ClO}_{2}^{-}&lt;\mathrm{ClO}^{-}$ is the correct
<br/> <br/>increasing order of Bronsted base. With increase in the number of oxygen atoms in the conjugate bases, the delocalisation of the $\pi$ bond becomes more and more extended. This results in decrease in the electron density. Consequently basicity also decreases.</div>


tags: ['Chemistry', 'Thermodynamics (C)', 'BITSAT', 'BITSAT 2011']
answer: <div class="solution">Condition of equilibrium, hence $\Delta \mathrm{G}=0$.</div>
source_db: MarksBatch2_P3.db
title:
what-is-the-free-energy-change-g-when-10-mole-of-water-at-10-0-c-and-1-atm-pressure-is-converted-into-steam-at-10-0-c-and-1-atm-pressure

slug:
what-is-the-free-energy-change-g-when-10-mole-of-water-at-10-0-c-and-1-atm-pressure-is-converted-into-steam-at-10-0-c-and-1-atm-pressure-25060

question:
<div class="question">What is the free energy change, $\Delta \mathrm{G}$, when 1.0 mole of water at $100^{\circ} \mathrm{C}$ and 1 atm pressure is converted into steam at $100^{\circ} \mathrm{C}$ and $1 \mathrm{~atm}$.<br/>pressure?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$540 \mathrm{cal}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">-9800 cal</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$9800 \mathrm{cal}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$0 \mathrm{cal}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$0 \mathrm{cal}$</span> </div>


title: what-is-the-hybridisation-of-crf-6-3
slug: what-is-the-hybridisation-of-crf-6-3-70452
question: <div class="question">What is the hybridisation of $\left[\mathrm{CrF}_6\right]^{3-}$ ?</div>
tags: ['Chemistry', 'Coordination Compounds', 'BITSAT', 'BITSAT 2022']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"> <br/>$s p^3 d$
<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"> <br/>$s p^3 d^2$
<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"> <br/>$d^2 s p^3$
<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"> <br/>$d^2 s p$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"> <br/>$d^2 s p^3$
<br/></span> </div>

answer:
<div class="solution">The electronic configuration of $\mathrm{Cr}$ is $[\mathrm{Ar}] 3 d^5 4 s^1$.
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/GRgumZbGj8rJxG3h3aRG8kzu9auCpNa7OEI4p3WJjE4.original.fullsize.png"/><br/> <br/>$\left[\mathrm{CrF}_6\right]^{3-}$ has $d^2 s p^3$-hybridisation and octahedral geometry.<img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/P530dI7r3bZQFwuTOvRrhNCiJwjR2dfidwr2pm055Pg.original.fullsize.png"/><br/></div>


title: what-is-the-magnetic-field-at-the-centre-of-arc-in-the-figure-below-1
slug: what-is-the-magnetic-field-at-the-centre-of-arc-in-the-figure-below-1-41392
tags: ['Physics', 'Magnetic Effects of Current', 'BITSAT', 'BITSAT 2017']
source_db: MarksBatch2_P3.db
question:
<div class="question"><p>What is the magnetic field at the centre of arc in the figure below? </p><p><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/30cae7fb-14d2-4b9e-95d7-83cb77ae1148-Capture34322.PNG" style="width: 300px; height: 160px;"/></p></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msub><mi>μ</mi><mn>0</mn></msub><mrow><mn>4</mn><mi>π</mi></mrow></mfrac><mo>·</mo><mfrac><mrow><mn>2</mn><mi>I</mi></mrow><mi>r</mi></mfrac><mfenced close="]" open="["><mrow><msqrt><mn>2</mn></msqrt><mo>+</mo><mi>π</mi></mrow></mfenced></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msub><mi>μ</mi><mn>0</mn></msub><mrow><mn>4</mn><mi>π</mi></mrow></mfrac><mo>·</mo><mfrac><mrow><mn>2</mn><mi>I</mi></mrow><mi>r</mi></mfrac><mfenced close="]" open="["><mrow><msqrt><mn>2</mn></msqrt><mo>+</mo><mfrac><mi>π</mi><mn>4</mn></mfrac></mrow></mfenced></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msub><mi>μ</mi><mn>0</mn></msub><mrow><mn>4</mn><mi>π</mi></mrow></mfrac><mo>·</mo><mfrac><mi>I</mi><mi>r</mi></mfrac><mfenced close="]" open="["><mrow><msqrt><mn>2</mn></msqrt><mo>+</mo><mi>π</mi></mrow></mfenced></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msub><mi>μ</mi><mn>0</mn></msub><mrow><mn>4</mn><mi>π</mi></mrow></mfrac><mo>·</mo><mfrac><mi>I</mi><mi>r</mi></mfrac><mfenced close="]" open="["><mrow><msqrt><mn>2</mn></msqrt><mo>+</mo><mfrac><mi>π</mi><mn>4</mn></mfrac></mrow></mfenced></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msub><mi>μ</mi><mn>0</mn></msub><mrow><mn>4</mn><mi>π</mi></mrow></mfrac><mo>·</mo><mfrac><mrow><mn>2</mn><mi>I</mi></mrow><mi>r</mi></mfrac><mfenced close="]" open="["><mrow><msqrt><mn>2</mn></msqrt><mo>+</mo><mfrac><mi>π</mi><mn>4</mn></mfrac></mrow></mfenced></math></span> </div>

answer:
<div class="solution"><p>Distance of straight path from <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>O</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mi>r</mi><msqrt><mn>2</mn></msqrt></mfrac></math></p><p>Hence, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><msub><mi>B</mi><mn>1</mn></msub><mo>+</mo><msub><mi>B</mi><mn>2</mn></msub></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><msub><mi>μ</mi><mn>0</mn></msub><mrow><mn>4</mn><mi>π</mi></mrow></mfrac><mo>·</mo><mfrac><mrow><mn>2</mn><mi>I</mi></mrow><mfrac><mi>r</mi><msqrt><mn>2</mn></msqrt></mfrac></mfrac><mo>+</mo><mfrac><msub><mi>μ</mi><mn>0</mn></msub><mrow><mn>4</mn><mi>π</mi></mrow></mfrac><mfrac><mrow><mn>2</mn><mi>π</mi><mi>I</mi></mrow><mi>r</mi></mfrac><mfenced><mfrac><mn>1</mn><mn>4</mn></mfrac></mfenced></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><msub><mi>μ</mi><mn>0</mn></msub><mrow><mn>4</mn><mi>π</mi></mrow></mfrac><mo>·</mo><mfrac><mrow><mn>2</mn><mi>I</mi></mrow><mi>r</mi></mfrac><mfenced close="]" open="["><mrow><msqrt><mn>2</mn></msqrt><mo>+</mo><mfrac><mi>π</mi><mn>4</mn></mfrac></mrow></mfenced></math></p></div>


title: what-is-the-maximum-wavelength-line-in-the-lyman-series-of-he-ion
slug: what-is-the-maximum-wavelength-line-in-the-lyman-series-of-he-ion-61945
tags: ['Chemistry', 'Structure of Atom', 'BITSAT', 'BITSAT 2020']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the maximum wavelength line in the Lyman series of $\mathrm{He}^{+}$ ion?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$3 R$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{1}{\mathrm{R}}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{1}{3 R}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of these</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{1}{3 R}$</span> </div>

answer:
<div class="solution">$\frac{1}{\lambda}=\mathrm{RZ}^{2}\left[\frac{1}{\mathrm{n}_{1}^{2}}-\frac{1}{\mathrm{n}_{2}^{2}}\right]=\mathrm{R} \times 2^{2}\left[\frac{1}{\mathrm{l}^{2}}-\frac{1}{2^{2}}\right]$
<br/> <br/>$\Rightarrow 3 \mathrm{R} ; \lambda=\frac{1}{3 \mathrm{R}}$</div>


title: what-is-the-moment-of-inertia-of-a-solid-sphere-of-density-and-radius-r-about-its-diameter
slug: what-is-the-moment-of-inertia-of-a-solid-sphere-of-density-and-radius-r-about-its-diameter-92197
tags: ['Physics', 'Rotational Motion', 'BITSAT', 'BITSAT 2012']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the moment of inertia of a solid sphere of density $\rho$ and radius $\mathrm{R}$ about its diameter?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{105}{176} \mathrm{R}^{5} \rho$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{105}{176} \mathrm{R}^{2} \rho$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{176}{105} \mathrm{R}^{5} \rho$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{176}{105} \mathrm{R}^{2} \rho$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{176}{105} \mathrm{R}^{5} \rho$</span> </div>

answer:
<div class="solution">For solid sphere
<br/>$\begin{array}{l}
<br/>I=\frac{2}{5} M R^{2}=\frac{2}{5}\left(\frac{4}{3} \pi R^{3} \rho\right) R^{2} \\
<br/>\rho=\frac{176}{105} R^{5} \rho
<br/>\end{array}$</div>


title: what-is-the-product-of-the-following-reaction-2
slug: what-is-the-product-of-the-following-reaction-2-23802
tags: ['Chemistry', 'Aldehydes and Ketones', 'BITSAT', 'BITSAT 2020']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the product of the following reaction?
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/pQ7IBEBMrqzBbz1QZpMaIkEUWs0CnyFU0U_uJ068Ssg.original.fullsize.png"/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/AlyRsugl2IoRJy1hcZZ2p6ZYHrL0yvXgzHn1kVmZocc.original.fullsize.png"/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/edR8rYQf6MdJW26RChY3PMTpGzEU_6zrDrrjBJWjgiM.original.fullsize.png"/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/4rqqJNUhVkyweWL0yOPy5ks8mETXGl4x9vvOy7WPhD0.original.fullsize.png"/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/vozZcFB5-qITtmGZoLyv77aqiEJy3K7C07q-HNxrqz0.original.fullsize.png"/></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/AlyRsugl2IoRJy1hcZZ2p6ZYHrL0yvXgzHn1kVmZocc.original.fullsize.png"/></span> </div>

answer:
<div class="solution">Only-CHO group reacts with CN $^{-}$ ion and the reaction is
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/6RB5JXkPZDc5Amf_Qh9ic-EW_lg-l_qJujbNYoSiI8w.original.fullsize.png"/></div>


title: what-is-the-solution-of-fracd-yd-x2-y1-satisfying-y00
slug: what-is-the-solution-of-fracd-yd-x2-y1-satisfying-y00-68497
tags: ['Mathematics', 'Differential Equations', 'BITSAT', 'BITSAT 2010']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is the solution of \(\frac{d y}{d x}+2 y=1\) satisfying \(y(0)=0\) ?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">\(y=\frac{1-e^{-2 x}}{2}\)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">\(y=\frac{1+e^{-2 x}}{2}\)</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">\(y=1+e^x\)</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">\(y=\frac{1+e^x}{2}\)</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\(y=\frac{1-e^{-2 x}}{2}\)</span> </div>

answer:
<div class="solution">\(\begin{aligned}<br/>&amp; \frac{d y}{d x}+2 y=1 \Rightarrow \frac{d y}{d x}=1-2 y \\<br/>&amp; \int \frac{d y}{1-2 y}=\int d x-\frac{1}{2} \log |1-2 y|=x+C \\<br/>&amp; \text { at } x=0, y=0 ;-\frac{1}{2} \log 1=0+C \Rightarrow C=0 \\<br/>&amp; 1-2 y=e^{-2 x} \Rightarrow y=\frac{1-e^{-2 x}}{2}<br/>\end{aligned}\)</div>


tags: ['Mathematics', 'Three Dimensional Geometry', 'BITSAT', 'BITSAT 2012']
source_db: MarksBatch2_P4.db
title:
what-is-the-value-of-n-so-that-the-angle-between-the-lines-having-direction-ratios-111-and-1-1-n-is-6-0

slug:
what-is-the-value-of-n-so-that-the-angle-between-the-lines-having-direction-ratios-111-and-1-1-n-is-6-0-49592

question:
<div class="question">What is the value of $n$ so that the angle between the lines having direction ratios (1,1,1) and $(1,-1, n)$ is $60^{\circ} ?$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\sqrt{3}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\sqrt{6}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">3</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of these</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\sqrt{6}$</span> </div>

answer:
<div class="solution">If $\left(l_{1}, m_{1}, n_{1}\right)$ and $\left(l_{2}, m_{2}, n_{2}\right)$ are the direction ratios then angle between the lines is
<br/>$\cos \theta=\frac{l_{1} l_{2}+m_{1} m_{2}+n_{1} n_{2}}{\sqrt{l_{1}^{2}+m_{1}^{2}+n_{1}^{2}} \sqrt{l_{2}^{2}+m_{2}^{2}+n_{2}^{2}}}$
<br/>Here $l_{1}=1, m_{1}=1, n_{1}=1$ and
<br/>$l_{2}=1, m_{2}=-1, n_{2}=n$ and $\theta=60^{\circ}$
<br/>$\therefore \cos 60^{\circ}=\frac{1 \times 1+1 \times(-1)+1 \times n}{\sqrt{h^{2}+1^{2}+1^{2} \times} \sqrt{1^{2}+1^{2}+y^{2}}}$
<br/>$\Rightarrow \frac{1}{2}=\frac{1}{\sqrt{3} \sqrt{2+n^{2}}} \Rightarrow 3\left(2+n^{2}\right)=4 n^{2}$
<br/>$\Rightarrow n^{2}=6 \Rightarrow n=\pm \sqrt{6}$</div>


tags: ['Mathematics', 'Application of Derivatives', 'BITSAT', 'BITSAT 2016']
source_db: MarksBatch2_P4.db
title:
what-is-the-x-coordinate-of-the-point-on-the-curve-f-x-x-7-x-6-where-the-tangent-is-parallel-to-x-axis-1

slug:
what-is-the-x-coordinate-of-the-point-on-the-curve-f-x-x-7-x-6-where-the-tangent-is-parallel-to-x-axis-1-38664

question:
<div class="question">What is the $x$ -coordinate of the point on the curve $f(x)=\sqrt{x}(7 x-6),$ where the tangent is parallel to $\mathrm{x}$ -axis?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$-\frac{1}{3}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{2}{7}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{6}{7}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{1}{2}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{2}{7}$</span> </div>

answer:
<div class="solution">$f(x)=\sqrt{x}(7 x-6)=7 x^{3 / 2}-6 x^{1 / 2}$
<br/> <br/>$f^{\prime}(x)=7 \times \frac{3}{2} x^{1 / 2}-6 \times \frac{1}{2} x^{-1 / 2}$
<br/> <br/>When tangent is parallel to $x$ axis $f^{\prime}(x)=0$
<br/> <br/>or, $\quad \frac{21}{2} \mathrm{x}^{1 / 2}-3 \mathrm{x}^{-1 / 2}=0$
<br/> <br/>$\frac{21}{2} \sqrt{x}=\frac{3}{\sqrt{x}}$
<br/> <br/>or, $7 x=2 \Rightarrow x=\frac{2}{7}$</div>


title: what-is-x-in-the-following-conversion
slug: what-is-x-in-the-following-conversion-21105
tags: ['Chemistry', 'Aldehydes and Ketones', 'BITSAT', 'BITSAT 2020']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is $\mathrm{X}$ in the following conversion?
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/HJA0OD_Q3lEqfSyoMySnIw1PpgwpMW0PY5DE_R3kb3E.original.fullsize.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}, \mathrm{H}_{2} \mathrm{SO}_{4} / \mathrm{H}_{2} \mathrm{O}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{HIO}_{4}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\mathrm{PCC} / \mathrm{CH}_{2} \mathrm{Cl}_{2}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{OsO}_{4},\left(\mathrm{CH}_{3}\right)_{3} \mathrm{C.COOH},\left(\mathrm{CH}_{3}\right)_{3} \mathrm{COH}, \mathrm{OH}^{-}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{PCC} / \mathrm{CH}_{2} \mathrm{Cl}_{2}$</span> </div>

answer:
<div class="solution">Pyridinium chloro chromate selectively oxidises a primary alcohol to an aldehyde 
<br/> <br/>e.g. <img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/j9vKN7ZKGZI1qFcKzulkXU543FtIJ1Zvfdc0dILfwB0.original.fullsize.png"/></div>


title: what-is-x-in-the-following-reaction-al-s-naoh-aq-h-2-o-l-x-h-2-g
slug: what-is-x-in-the-following-reaction-al-s-naoh-aq-h-2-o-l-x-h-2-g-64794
tags: ['Chemistry', 'p Block Elements (Group 13 & 14)', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 1)']
source_db: MarksBatch2_P4.db
question:
<div class="question">What is $x$ in the following reaction?<br/>$\mathrm{Al}(\mathrm{s})+\mathrm{NaOH}(\mathrm{aq})+\mathrm{H}_2 \mathrm{O}(\mathrm{l}) \rightarrow x+\mathrm{H}_2(\mathrm{~g})$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"> $\mathrm{Na}_2\left[\mathrm{Al}(\mathrm{OH})_4\right]^{-}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\mathrm{Na}^{+}\left[\mathrm{Al}(\mathrm{OH})_4\right]^{-}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{Na}_2\left[\mathrm{Al}(\mathrm{OH})_6\right]^{-}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{Na}^{+}\left[\mathrm{Al}(\mathrm{OH})_6\right]^{-}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{Na}^{+}\left[\mathrm{Al}(\mathrm{OH})_4\right]^{-}$</span> </div>

answer:
<div class="solution">$2 \mathrm{Al}(\mathrm{s})+2 \mathrm{NaOH}(\mathrm{aq})+6 \mathrm{H}_2 \mathrm{O}(\mathrm{l}) \rightarrow$ $2 \mathrm{Na}^{+}\left[\mathrm{Al}(\mathrm{OH})_4\right]^{-}(\mathrm{aq})+3 \mathrm{H}_2(\mathrm{~g})$</div>


title: what-should-be-the-characteristic-of-fuse-wire
slug: what-should-be-the-characteristic-of-fuse-wire-88695
question: <div class="question">What should be the characteristic of fuse wire?</div>
tags: ['Physics', 'Current Electricity', 'BITSAT', 'BITSAT 2013']
source_db: MarksBatch2_P4.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">High melting point, high specific resistance.</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Low melting point, low specific resistance.</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">High melting point, low specific resistance.</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">Low melting point, high specific resistance.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Low melting point, high specific resistance.</span> </div>

answer:
<div class="solution">Fuse wire should be such that it melts immediatley when strong current flows through the circuit. The same is possible if its melting point is low and resistivity is high.</div>


tags: ['Physics', 'Gravitation', 'BITSAT', 'BITSAT 2016']
source_db: MarksBatch2_P4.db
title:
what-should-be-the-velocity-of-rotation-of-earth-due-to-rotation-about-its-own-axis-so-that-the-weight-of-a-person-becomes-5-3-of-the-present-weight-a

slug:
what-should-be-the-velocity-of-rotation-of-earth-due-to-rotation-about-its-own-axis-so-that-the-weight-of-a-person-becomes-5-3-of-the-present-weight-a-51054

question:
<div class="question">What should be the velocity of rotation of earth due to rotation about its own axis so that the weight of a person becomes $\frac{3}{5}$ of the present weight at the equator. Equatorial radius of the earth is $6400 \mathrm{~km}$.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$8.7 \times 10^{-7} \mathrm{rad} / \mathrm{s}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$7.8 \times 10^{-4} \mathrm{rad} / \mathrm{s}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$6.7 \times 10^{-4} \mathrm{rad} / \mathrm{s}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$7.4 \times 10^{-3} \mathrm{rad} / \mathrm{s}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$7.8 \times 10^{-4} \mathrm{rad} / \mathrm{s}$</span> </div>

answer:
<div class="solution">True weight at equator, $W=m g$ Observed weight at equator,
<br/> <br/>$$
<br/> <br/>\mathrm{W}^{\prime}=\mathrm{mg}^{\prime}=\frac{3}{5} \mathrm{mg}
<br/> <br/>$$
<br/> <br/>At equator, latitude $\lambda=0$ Using the formula,
<br/> <br/>$$
<br/> <br/>\begin{array}{l}
<br/> <br/>\mathrm{mg}^{\prime}=\mathrm{mg}-\mathrm{mR} \omega^{2} \cos ^{2} \lambda \\
<br/> <br/>\frac{3}{5} \mathrm{mg}=\mathrm{mg}-\mathrm{mR} \omega^{2} \cos ^{2} 0=\mathrm{mg}-\mathrm{mR} \omega^{2} \\
<br/> <br/>\Rightarrow \mathrm{mR} \omega^{2}=\mathrm{mg}-\frac{3}{5} \mathrm{mg}=\frac{2}{5} \mathrm{mg} \\
<br/> <br/>\therefore \quad \omega=\left(\frac{2}{5} \frac{\mathrm{g}}{\mathrm{R}}\right)^{1 / 2} \\
<br/> <br/>=\left(\frac{2 \times 9.8}{5 \times 6.4 \times 10^{6}}\right)^{1 / 2}=7.8 \times 10^{-4} \mathrm{rad} / \mathrm{s}
<br/> <br/>\end{array}
<br/> <br/>$$</div>


tags: ['Chemistry', 'Electrochemistry', 'BITSAT', 'BITSAT 2019']
source_db: MarksBatch2_P4.db
title:
what-time-in-sec-is-required-for-depositing-all-the-silver-present-in-125-ml-of-1-m-agno-3-solution-by-passing-a-current-of-241-25-a-given-1-f-96500-c

slug:
what-time-in-sec-is-required-for-depositing-all-the-silver-present-in-125-ml-of-1-m-agno-3-solution-by-passing-a-current-of-241-25-a-given-1-f-96500-c-56678

question:
<div class="question">What time in sec is required for depositing all the silver present in <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>125</mn><mo> </mo><mi>ml</mi></math> of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo> </mo><mi mathvariant="normal">M</mi><mo> </mo><msub><mi>AgNO</mi><mn>3</mn></msub></math> solution by passing a current of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>241</mn><mo>.</mo><mn>25</mn></math> A (Given <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo> </mo><mi mathvariant="normal">F</mi><mo>=</mo><mo> </mo><mn>96500</mn><mo> </mo><mi mathvariant="normal">C</mi></math>)</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1000</mn></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn></math></span> </div>

answer:
<div class="solution"><p>Given, <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>125</mn><mo> </mo><mi>ml</mi></math> of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo> </mo><mi mathvariant="normal">M</mi><mo> </mo><msub><mi>AgNO</mi><mn>3</mn></msub></math></p><p>which is equal to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13</mn><mo>.</mo><mn>5</mn><mo> </mo><mi mathvariant="normal">g</mi></math> of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Ag</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∵</mo><mo> </mo><mn>1000</mn><mo> </mo><mi>ml</mi></math> of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>AgNO</mi><mn>3</mn></msub><mo>=</mo><mn>108</mn><mo> </mo><mi mathvariant="normal">g</mi></math> of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Ag</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mo> </mo><mn>125</mn><mo> </mo><mi>ml</mi></math> of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>AgNO</mi><mn>3</mn></msub><mo>=</mo><mfrac><mrow><mn>108</mn><mo>×</mo><mn>125</mn></mrow><mn>1000</mn></mfrac><mo>=</mo><mn>13</mn><mo>.</mo><mn>5</mn><mo> </mo><mi mathvariant="normal">g</mi></math></p><p>Also, <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∵</mo><mo> </mo><mn>108</mn><mo> </mo><mi mathvariant="normal">g</mi></math> of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Ag</mi></math> is deposited by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>96500</mn><mo> </mo><mi mathvariant="normal">C</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mo> </mo><mn>13</mn><mo>.</mo><mn>5</mn><mo> </mo><mi mathvariant="normal">g</mi></math> of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Ag</mi></math> is deposited by <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><mn>96500</mn><mo>×</mo><mn>13</mn><mo>.</mo><mn>5</mn></mrow><mn>108</mn></mfrac><mo>=</mo><mn>12062</mn><mo>.</mo><mn>5</mn><mo> </mo><mi mathvariant="normal">C</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∵</mo><mo> </mo><mi mathvariant="normal">Q</mi><mo>=</mo><mi>it</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mo> </mo><mi mathvariant="normal">t</mi></math> (time) <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mi mathvariant="normal">Q</mi><mo>/</mo><mi mathvariant="normal">i</mi><mo>=</mo><mfrac><mrow><mn>12062</mn><mo>.</mo><mn>50</mn></mrow><mrow><mn>241</mn><mo>.</mo><mn>25</mn></mrow></mfrac><mo>,</mo><mo> </mo><mi mathvariant="normal">t</mi><mo>=</mo><mn>50</mn><mo> </mo><mi>sec</mi></math></p></div>


tags: ['Physics', 'Laws of Motion', 'BITSAT', 'BITSAT 2022']
source_db: MarksBatch2_P4.db
title:
what-will-be-the-acceleration-due-to-gravity-at-a-depth-d-where-g-is-acceleration-due-to-gravity-on-the-surface-of-earth

slug:
what-will-be-the-acceleration-due-to-gravity-at-a-depth-d-where-g-is-acceleration-due-to-gravity-on-the-surface-of-earth-55200

question:
<div class="question">What will be the acceleration due to gravity at a depth $d$, where $g$ is acceleration due to gravity on the surface of earth?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"> <br/>$\frac{g}{\left[1+\frac{d}{R}\right]^2}$
<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"> <br/>$g\left[1-\frac{2 d}{R}\right]$
<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"> <br/>$\frac{g}{\left[1-\frac{d}{R}\right]^2}$
<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"> <br/>$g\left[1-\frac{d}{R}\right]$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"> <br/>$g\left[1-\frac{d}{R}\right]$</span> </div>

answer:
<div class="solution">Acceleration due to gravity at the surface of earth,
<br/>$$
<br/>g=\frac{G M}{R^2}=\frac{4}{3} \pi \rho G R
<br/>$$
<br/>$$
<br/>\left[\because M=\frac{4}{3} \pi R^3 \cdot \rho\right]
<br/>$$
<br/>Where, $\rho=$ density of earth.
<br/>Acceleration due to gravity at depth $d$ from the surface of earth,
<br/>$$
<br/>g^{\prime}=\frac{4}{3} \pi \rho G(R-d)
<br/>$$
<br/>From Eqs. (i) and (ii), we get
<br/>$$
<br/>g^{\prime}=g\left[1-\frac{d}{R}\right]
<br/>$$</div>


title: what-will-be-the-correct-structural-formula-of-product-for-the-following-reaction-1
slug: what-will-be-the-correct-structural-formula-of-product-for-the-following-reaction-1-18346
tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'JEE Main']
source_db: MarksBatch2_P4.db
question:
<div class="question">What will be the correct structural formula of product for the following reaction?
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/V3LgFsWGGIKApy3j6WDEY54C0iyTYKjCc8e9SpLsG-Q.original.fullsize.png"/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/pZixVQfoDTi0nX_u8Bi4_-nRtsLAERh0KEZE4vog_1A.original.fullsize.png"/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/7Yel2pb7naJ2DaqhRWzCgVexiELV35qcMAShgsJ82HY.original.fullsize.png"/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/egTcNnKNzaIhSn5qYQO3RJBy0tA2RUPMlW0lkju-27o.original.fullsize.png"/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/YFYU1znvUjbm0t95-ctNyR91euDkn0enNOHJs9_6n3M.original.fullsize.png"/></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/pZixVQfoDTi0nX_u8Bi4_-nRtsLAERh0KEZE4vog_1A.original.fullsize.png"/></span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/6r3ZJWMEAxdKsOkbL-Tey38eEBO4MjBUKugUmVGRWko.original.fullsize.png"/></div>


title: what-will-be-the-main-product-when-acetylene-reacts-with-hypochlorous-acid
slug: what-will-be-the-main-product-when-acetylene-reacts-with-hypochlorous-acid-24347
tags: ['Chemistry', 'Hydrocarbons', 'BITSAT', 'BITSAT 2013']
source_db: MarksBatch2_P4.db
question:
<div class="question">What will be the main product when acetylene reacts with hypochlorous acid?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Trichloroacetaldehyde</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Acetaldehyde</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Dichloroacetaldehyde</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Chloro acetaldehyde</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Dichloroacetaldehyde</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/hlf3Y_Nq4pgoEVLkcSzd7h4OtbMylBswqfkga5LeOjk.original.fullsize.png"/></div>


title: what-will-be-the-product-in-the-following-reaction-1
slug: what-will-be-the-product-in-the-following-reaction-1-97031
tags: ['Chemistry', 'Hydrocarbons', 'JEE Main']
source_db: MarksBatch2_P4.db
question:
<div class="question">What will be the product in the following reaction?<br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/M5PDgDZgR7yWLF0NYjclJeu7zaPcBOcfaNat3dn-9Vk.original.fullsize.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/PS-eg3QoWlcdu1NJDDRT036PRrj_vOcUdB5EjClZO1Q.original.fullsize.png"/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/bExdh6MZWorzLtDcUXk2dR1ri44J9QpxJuXMWQbGaQk.original.fullsize.png"/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/-ZzrSMPrqyT-7jwsaSfj8vZYT0MI0RSuRgjzUTEXLbs.original.fullsize.png"/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/vrblTDUSBewIsAqInLUUol-OVXjIzA64-OBPEpHRK0A.original.fullsize.png"/></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/-ZzrSMPrqyT-7jwsaSfj8vZYT0MI0RSuRgjzUTEXLbs.original.fullsize.png"/></span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/Uk9FsHOQXi_q1dhI03SFpe4R007LlzJFFG7fPR8qgAI.original.fullsize.png"/></div>


title: what-will-happen-when-dglucose-is-treated-with-methanolic-hcl-followed-by-tollens-reagent
slug: what-will-happen-when-dglucose-is-treated-with-methanolic-hcl-followed-by-tollens-reagent-60458
tags: ['Chemistry', 'Aldehydes and Ketones', 'BITSAT', 'BITSAT 2016']
source_db: MarksBatch2_P4.db
question:
<div class="question">What will happen when D-(+)-glucose is treated with methanolic - HCl followed by Tollens' reagent?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">A black ppt. will be formed</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">A red ppt. will be formed</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">A green colour will appear</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">No characteristic colour or ppt. will be formed.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">No characteristic colour or ppt. will be formed.</span> </div>

answer:
<div class="solution">Reaction of $\mathrm{D}-(+)$ -glucose with methanolic $-\mathrm{HCl}$ leads to formation of methyl glucoside $\left(\mathrm{C}_{1}-\mathrm{OH}\right.$ group is methylated) which, being acetal, is not hydrolysable by base, so it will not respond Tollens'reagent.</div>


tags: ['Physics', 'Dual Nature of Matter', 'BITSAT', 'BITSAT 2015']
source_db: MarksBatch2_P4.db
title:
when-050-a-xrays-strike-a-material-the-photoelectrons-from-the-k-shell-are-observed-to-move-in-a-circle-of-radius-23-mm-in-a-magnetic-field-of-2-1-0-2

slug:
when-050-a-xrays-strike-a-material-the-photoelectrons-from-the-k-shell-are-observed-to-move-in-a-circle-of-radius-23-mm-in-a-magnetic-field-of-2-1-0-2-13622

question:
<div class="question">When $0.50 Ã$ X-rays strike a material, the photoelectrons from the $\mathrm{k}$ shell are observed to move in a circle of radius $23 \mathrm{~mm}$ in a magnetic field of $2 \times 10^{-2}$ tesla acting perpendicularly to the direction of emission of photoelectrons. What is the binding energy of k-shell electrons?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$3.5 \mathrm{keV}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$6.2 \mathrm{keV}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$2.9 \mathrm{keV}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$5.5 \mathrm{keV}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$6.2 \mathrm{keV}$</span> </div>

answer:
<div class="solution">As we know,
<br/> <br/>$$
<br/> <br/>\mathrm{F}=\mathrm{qvB}=\mathrm{m} \frac{\mathrm{v}^{2}}{\mathrm{R}} \Rightarrow \mathrm{v}=\frac{\mathrm{q}}{\mathrm{m}} \mathrm{BR}
<br/> <br/>$$
<br/> <br/>The kinetic energy of the photoelectron
<br/> <br/>$$
<br/> <br/>\begin{array}{l}
<br/> <br/>=\frac{1}{2} m v^{2}=\frac{1}{2} \frac{e^{2} B^{2} R^{2}}{m} \\
<br/> <br/>=\frac{1}{2} \frac{\left(1.6 \times 10^{-19}\right)^{2}\left(2 \times 10^{-2}\right)^{2}\left(23 \times 10^{-3}\right)^{2}}{\left(9.1 \times 10^{-31}\right)} \\
<br/> <br/>=2.97 \times 10^{-15} \mathrm{~J} \\
<br/> <br/>=\frac{2.97 \times 10^{-15}}{1.6 \times 10^{-19}}=18.36 \mathrm{keV}
<br/> <br/>\end{array}
<br/> <br/>$$
<br/> <br/>Fnergy of the incident $\mathrm{n}=\frac{\mathrm{hc}}{\lambda}$
<br/> <br/>$$
<br/> <br/>=\frac{12.4}{0.50}=24.8 \mathrm{keV}
<br/> <br/>$$
<br/> <br/>Therefore, Binding energy $=24.8-18.6=$ $6.2 \mathrm{keV}$</div>


tags: ['Physics', 'Capacitance', 'JEE Main']
source_db: MarksBatch2_P4.db
title:
when-a-capacitor-is-fully-charged-as-shown-in-the-following-figure-then-current-drawn-from-the-cell-is-1

slug:
when-a-capacitor-is-fully-charged-as-shown-in-the-following-figure-then-current-drawn-from-the-cell-is-1-66651

question:
<div class="question"><p>When a capacitor is fully charged as shown in the following figure, then current drawn from the cell is</p><p><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/9e6da9e7-b415-4494-b2d5-5afaa5c11870-image.png" style="width: 230px; height: 156px;"/></p></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo> </mo><mi>mA</mi></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>5</mn><mo> </mo><mi>mA</mi></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo> </mo><mi>mA</mi></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo> </mo><mi>mA</mi></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>5</mn><mo> </mo><mi>mA</mi></math></span> </div>

answer:
<div class="solution"><p>When capacitor is fully charged, then it acts like a open switch, therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo> </mo><mi>kΩ</mi></math> resistor has no use. So, rest of the resistances <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo> </mo><mi>kΩ</mi><mo>,</mo><mo> </mo><mn>7</mn><mo> </mo><mi>kΩ</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo> </mo><mi>kΩ</mi></math> will be in series. Hence, current drawn from cell</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mo>=</mo><mfrac><mn>10</mn><mrow><mfenced><mrow><mn>4</mn><mo>+</mo><mn>7</mn><mo>+</mo><mn>9</mn></mrow></mfenced><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup></mrow></mfrac><mo>=</mo><mfrac><mn>10</mn><mrow><mn>20</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup></mrow></mfrac><mo>=</mo><mn>0</mn><mo>.</mo><mn>5</mn><mo> </mo><mi>mA</mi></math></p></div>


tags: ['Physics', 'Capacitance', 'BITSAT', 'BITSAT 2019']
source_db: MarksBatch2_P4.db
title:
when-a-capacitor-is-fully-charged-as-shown-in-the-following-figure-then-current-drawn-from-the-cell-is

slug:
when-a-capacitor-is-fully-charged-as-shown-in-the-following-figure-then-current-drawn-from-the-cell-is-94316

question:
<div class="question"><p>When a capacitor is fully charged as shown in the following figure, then current drawn from the cell is</p><p><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/9e6da9e7-b415-4494-b2d5-5afaa5c11870-image.png" style="width: 230px; height: 156px;"/></p></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo> </mo><mi>mA</mi></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>5</mn><mo> </mo><mi>mA</mi></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo> </mo><mi>mA</mi></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo> </mo><mi>mA</mi></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>5</mn><mo> </mo><mi>mA</mi></math></span> </div>

answer:
<div class="solution"><p>When capacitor is fully charged, then it acts like a open switch, therefore <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo> </mo><mi>kΩ</mi></math> resistor has no use. So, rest of the resistances <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo> </mo><mi>kΩ</mi><mo>,</mo><mo> </mo><mn>7</mn><mo> </mo><mi>kΩ</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo> </mo><mi>kΩ</mi></math> will be in series. Hence, current drawn from cell</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mo>=</mo><mfrac><mn>10</mn><mrow><mfenced><mrow><mn>4</mn><mo>+</mo><mn>7</mn><mo>+</mo><mn>9</mn></mrow></mfenced><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup></mrow></mfrac><mo>=</mo><mfrac><mn>10</mn><mrow><mn>20</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup></mrow></mfrac><mo>=</mo><mn>0</mn><mo>.</mo><mn>5</mn><mo> </mo><mi>mA</mi></math></p></div>


title: when-a-crystal-of-caustic-soda-is-exposed-to-air-a-liquid-layer-is-deposited-because
slug: when-a-crystal-of-caustic-soda-is-exposed-to-air-a-liquid-layer-is-deposited-because-92741
tags: ['Chemistry', 's Block Elements', 'BITSAT', 'BITSAT 2011']
source_db: MarksBatch2_P4.db
question:
<div class="question">When a crystal of caustic soda is exposed to air, a liquid layer is deposited because :</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Crystal loses water</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Crystal absorbs moisture and $\mathrm{CO}_{2}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Crystal melts</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Crystal sublimes</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Crystal absorbs moisture and $\mathrm{CO}_{2}$</span> </div>

answer:
<div class="solution">It is hygroscopic and deliquescent and hence absorbs moisture and $\mathrm{CO}_{2}$ to form $\mathrm{Na}_{2} \mathrm{CO}_{3}$<br/>$$<br/>2 \mathrm{NaOH}+\mathrm{CO}_{2} \longrightarrow \mathrm{Na}_{2} \mathrm{CO}_{3}+\mathrm{H}_{2} \mathrm{O}<br/>$$</div>


tags: ['Physics', 'Wave Optics', 'BITSAT', 'BITSAT 2009']
source_db: MarksBatch2_P4.db
title:
when-a-mica-sheet-of-thickness-7-microns-and-16-is-placed-in-the-path-of-one-of-interfering-beams-in-the-biprism-experiment-then-the-central-fringe-ge

slug:
when-a-mica-sheet-of-thickness-7-microns-and-16-is-placed-in-the-path-of-one-of-interfering-beams-in-the-biprism-experiment-then-the-central-fringe-ge-75517

question:
<div class="question">When a mica sheet of thickness 7 microns and $\mu=1.6$ is placed in the path of one of interfering beams in the biprism experiment then the central fringe gets at the position of seventh bright fringe. The wavelength of light used will be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$4000 \mathrm{~A}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$5000 \AA$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$6000 \mathrm{~A}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$7000 \AA$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$6000 \mathrm{~A}$</span> </div>

answer:
<div class="solution">$\lambda=\frac{(\mu-1) \mathrm{t}}{\mathrm{n}}$<br/>According to question<br/>$$<br/>\mathrm{n}=7, \mu=1.6, \mathrm{t}=7 \times 10^{-6} \mathrm{~meter}<br/>$$<br/>From eqs. (1) and $(2), \lambda=6 \times 10^{-7}$ meter</div>


tags: ['Physics', 'Waves and Sound', 'BITSAT', 'BITSAT 2014']
source_db: MarksBatch2_P4.db
title:
when-a-string-is-divided-into-three-segments-of-length-l-1-l-2-and-l-3-the-fundamental-frequencies-of-these-three-segments-are-v-1-v-2-and-v-3-respect

slug:
when-a-string-is-divided-into-three-segments-of-length-l-1-l-2-and-l-3-the-fundamental-frequencies-of-these-three-segments-are-v-1-v-2-and-v-3-respect-95270

question:
<div class="question">When a string is divided into three segments of length $l_{1}, l_{2},$ and $l_{3}$, the fundamental frequencies of these three segments are $v_{1}, v_{2}$ and $v_{3}$ respectively. The original fundamental frequency
<br/> <br/>(v) of the string is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\quad \sqrt{v}=\sqrt{v_{1}}+\sqrt{v_{2}}+\sqrt{v_{3}}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$v=v_{1}+v_{2}+v_{3}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{1}{v}=\frac{1}{v_{1}}+\frac{1}{v_{2}}+\frac{1}{v_{3}}$.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{1}{\sqrt{v}}=\frac{1}{\sqrt{v_{1}}}+\frac{1}{\sqrt{v_{2}}}+\frac{1}{\sqrt{v_{3}}}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{1}{v}=\frac{1}{v_{1}}+\frac{1}{v_{2}}+\frac{1}{v_{3}}$.</span> </div>

answer:
<div class="solution">Fundamental frequency is given by
<br/> <br/>$$
<br/> <br/>v=\frac{1}{2 l} \sqrt{\frac{T}{\mu}} \Rightarrow v \propto \frac{1}{l} \Rightarrow P \propto \frac{1}{v}
<br/> <br/>$$
<br/> <br/>Since, $P$ divided into $l_{1}, l_{2}$ and $l_{3}$ segments Here $l=l_{1}+l_{2}+l_{3}$
<br/> <br/>So $\quad \frac{1}{v}=\frac{1}{v_{1}}+\frac{1}{v_{2}}+\frac{1}{v_{3}}$</div>


title: when-aqueous-solutions-of-borax-is-acidified-with-hcl-we-get
slug: when-aqueous-solutions-of-borax-is-acidified-with-hcl-we-get-81909
tags: ['Chemistry', 'p Block Elements (Group 15, 16, 17 & 18)', 'BITSAT', 'BITSAT 2017']
source_db: MarksBatch2_P4.db
question:
<div class="question">When aqueous solutions of borax is acidified with <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>HCl</mi></math>, we get</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">B</mi><mn>2</mn></msub><msub><mi mathvariant="normal">H</mi><mn>6</mn></msub></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">H</mi><mn>3</mn></msub><msub><mi>BO</mi><mn>3</mn></msub></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">B</mi><mn>2</mn></msub><msub><mi mathvariant="normal">O</mi><mn>3</mn></msub></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">All of these</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">H</mi><mn>3</mn></msub><msub><mi>BO</mi><mn>3</mn></msub></math></span> </div>

answer:
<div class="solution"><p>When aqueous solution of borax <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><msub><mi>Na</mi><mn>2</mn></msub><msub><mi mathvariant="normal">B</mi><mn>4</mn></msub><msub><mi mathvariant="normal">O</mi><mn>7</mn></msub></mrow></mfenced></math> is acidified<br/>with <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>HCl</mi></math>, we get <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">H</mi><mn>3</mn></msub><msub><mi>BO</mi><mn>3</mn></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>NaCl</mi></math> as follows</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><munder><mrow><msub><mi>Na</mi><mn>2</mn></msub><msub><mi mathvariant="normal">B</mi><mn>4</mn></msub><msub><mi mathvariant="normal">O</mi><mn>7</mn></msub></mrow><mi>Borox</mi></munder><mo>+</mo><mn>2</mn><mi>HCl</mi><mo>+</mo><mn>5</mn><msub><mi mathvariant="normal">H</mi><mn>2</mn></msub><mi mathvariant="normal">O</mi><mo>⟶</mo><mn>2</mn><mi>NaCl</mi><mo>+</mo><munder><mrow><mn>4</mn><msub><mi mathvariant="normal">H</mi><mn>3</mn></msub><msub><mi>BO</mi><mn>3</mn></msub></mrow><mrow><mi>Boric</mi><mo> </mo><mi>acid</mi></mrow></munder></math></p><p>Boric acid is not a proticacid it does not give <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi mathvariant="normal">H</mi><mo>+</mo></msup></math> ion accepts a pair of electrons and acts as a Lewis acid.</p></div>


tags: ['Chemistry', 'Practical Chemistry', 'BITSAT', 'BITSAT 2021']
source_db: MarksBatch2_P4.db
title:
when-c-2-h-2-ch-4-and-c-2-h-4-pass-through-a-test-tube-which-has-ammonical-cu-2-cl-2-find-out-which-gas-comes-out-unaffected-from-test-tube

slug:
when-c-2-h-2-ch-4-and-c-2-h-4-pass-through-a-test-tube-which-has-ammonical-cu-2-cl-2-find-out-which-gas-comes-out-unaffected-from-test-tube-83915

question:
<div class="question">When $\mathrm{C}_{2} \mathrm{H}_{2}, \mathrm{CH}_{4}$ and $\mathrm{C}_{2} \mathrm{H}_{4}$ pass through a test tube which has ammonical $\mathrm{Cu}_{2} \mathrm{Cl}_{2}$, find out which gas comes out unaffected from test tube?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{C}_{2} \mathrm{H}_{2}$ and $\mathrm{CH}_{4}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{C}_{2} \mathrm{H}_{2}$ and $\mathrm{C}_{2} \mathrm{H}_{4}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\mathrm{C}_{2} \mathrm{H}_{4}$ and $\mathrm{CH}_{4}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{C}_{2} \mathrm{H}_{2}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{C}_{2} \mathrm{H}_{4}$ and $\mathrm{CH}_{4}$</span> </div>

answer:
<div class="solution">$\mathrm{C}_{2} \mathrm{H}_{2}$ forms copper acetylide with ammonical $\mathrm{Cu}_{2} \mathrm{Cl}_{2}$
<br/> <br/>$\begin{array}{l}
<br/> <br/>\mathrm{Cu}_{2} \mathrm{Cl}_{2}+2 \mathrm{NH}_{4} \mathrm{OH} \rightarrow \mathrm{Cu}_{2} \mathrm{O}+\mathrm{H}_{2} \mathrm{O}+2 \mathrm{NH}_{4} \mathrm{Cl} \\
<br/> <br/>\mathrm{Cu}_{2} \mathrm{O}+\mathrm{C}_{2} \mathrm{H}_{2} \rightarrow \underset{\text { (copper acetylide) }}{\mathrm{Cu}_{2} \mathrm{C}_{2}}+\mathrm{H}_{2} \mathrm{O}
<br/> <br/>\end{array}$</div>


title: when-chlorine-water-is-exposed-to-sunlight-o-2-is-liberated-hence
slug: when-chlorine-water-is-exposed-to-sunlight-o-2-is-liberated-hence-58241
tags: ['Chemistry', 'Hydrogen', 'BITSAT', 'BITSAT 2012']
source_db: MarksBatch2_P4.db
question:
<div class="question">When chlorine water is exposed to sunlight, $\mathrm{O}_{2}$ is liberated. Hence,</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">hydrogen has little affinity to $\mathrm{O}_{2}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">hydrogen has more affinity to $\mathrm{O}_{2}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">hydrogen has more affinity to chlorine</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">it is a reducing agent</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">hydrogen has more affinity to chlorine</span> </div>

answer:
<div class="solution">$\mathrm{Cl}_{2}+\mathrm{H}_{2} \mathrm{O} \rightarrow 2 \mathrm{HCl}+\frac{1}{2} \mathrm{O}_{2}$
<br/>Hydrogen has more affinity for chlorine.</div>


tags: ['Chemistry', 'd and f Block Elements', 'BITSAT', 'BITSAT 2018']
source_db: MarksBatch2_P4.db
title:
when-dil-sulphuric-acid-reacts-with-aqueous-solution-of-potassium-chromate-the-colour-changes-from-yellow-to-orange-this-shows-that

slug:
when-dil-sulphuric-acid-reacts-with-aqueous-solution-of-potassium-chromate-the-colour-changes-from-yellow-to-orange-this-shows-that-17727

question:
<div class="question">When dil. sulphuric acid reacts with aqueous solution of potassium chromate, the colour changes from yellow to orange. This shows that</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">chromate ions reduced</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">chromate ions are oxidised</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">monocentric complex is converted into dicentric complex</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">oxygen gets removed from chromate ions</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">monocentric complex is converted into dicentric complex</span> </div>

answer:
<div class="solution"><p>On acidification of potassium chromate solution, yellow colour changes to orange colour due to formation of dichromate which suggests that monocentric complex is converted into dicentric complex.</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><msub><mi mathvariant="normal">K</mi><mn>2</mn></msub><msub><mi>CrO</mi><mn>4</mn></msub><mo>+</mo><munder><mrow><msub><mi mathvariant="normal">H</mi><mn>2</mn></msub><msub><mi>SO</mi><mn>4</mn></msub></mrow><mfenced><mtext>Dil.</mtext></mfenced></munder><mo>⟶</mo><msub><mi mathvariant="normal">K</mi><mn>2</mn></msub><msub><mi>Cr</mi><mn>2</mn></msub><msub><mi mathvariant="normal">O</mi><mn>7</mn></msub><mo>+</mo><mo> </mo><msub><mi mathvariant="normal">K</mi><mn>2</mn></msub><msub><mi>SO</mi><mn>4</mn></msub><mo>+</mo><msub><mi mathvariant="normal">H</mi><mn>2</mn></msub><mi mathvariant="normal">O</mi></math></p></div>


title: when-esters-are-hydrolysed-the-product-gives-hydrogen-ions-the-product-which-gives-hydrogen-ion-is
tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'BITSAT', 'BITSAT 2009']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">acid</span> </div>
source_db: MarksBatch2_P4.db
slug:
when-esters-are-hydrolysed-the-product-gives-hydrogen-ions-the-product-which-gives-hydrogen-ion-is-10308

question:
<div class="question">When esters are hydrolysed the product gives hydrogen ions. The product which gives hydrogen ion is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">acid</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">alcohol</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">both</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">either acid or alcohol</span> </li> </ul>

answer:
<div class="solution">When esters are hydrolysed, then acid and alcohol are formed, where acid gives hydrogen ion.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/cRFzrpLXSMJr5Vq_qgpy_9Lc9_1GFQmkfdWG-0jYzmY.original.fullsize.png"/></div>


title: when-ethylamine-react-with-sodium-metal-the-gas-evolved-is
slug: when-ethylamine-react-with-sodium-metal-the-gas-evolved-is-90598
question: <div class="question">When ethylamine react with sodium metal, the gas evolved is</div>
tags: ['Chemistry', 'Amines', 'BITSAT', 'BITSAT 2010']
source_db: MarksBatch2_P4.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\mathrm{H}_{2}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{C}_{2} \mathrm{H}_{5}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{N}_{2}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{NH}_{3}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{H}_{2}$</span> </div>

answer:
<div class="solution">When ethylamine is heated with sodium metal, then hydrogen gas is evolved. $2 \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NH}_{2}+2 \mathrm{Na} \longrightarrow$<br/>$$<br/>2 \mathrm{C}_{2} \mathrm{H}_{5} \overline{\mathrm{N}} \mathrm{HNa}^{+}+\mathrm{H}_{2} \uparrow<br/>$$</div>


tags: ['Chemistry', 'Practical Chemistry', 'BITSAT', 'BITSAT 2018']
source_db: MarksBatch2_P4.db
title:
when-h-2-s-gas-is-passed-into-a-mixture-of-mn-2-ni-2-cu-2-and-hg-2-ion-in-an-acidified-aqueous-solution-the-precipitates-formed-are

slug:
when-h-2-s-gas-is-passed-into-a-mixture-of-mn-2-ni-2-cu-2-and-hg-2-ion-in-an-acidified-aqueous-solution-the-precipitates-formed-are-47651

question:
<div class="question">When <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">H</mi><mn>2</mn></msub><mi mathvariant="normal">S</mi></math> gas is passed into a mixture of <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>Mn</mi><mrow><mn>2</mn><mo>+</mo></mrow></msup><mo>,</mo><mo> </mo><msup><mi>Ni</mi><mrow><mn>2</mn><mo>+</mo></mrow></msup><mo>,</mo><mo> </mo><msup><mi>Cu</mi><mrow><mn>2</mn><mo>+</mo></mrow></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>Hg</mi><mrow><mn>2</mn><mo>+</mo></mrow></msup></math> ion in an acidified aqueous solution, the precipitates formed are</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>CuS</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>HgS</mi></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>MnS</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>CuS</mi></math></p></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>MnS</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>NiS</mi></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>NiS</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>HgS</mi></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>CuS</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>HgS</mi></math></span> </div>

answer:
<div class="solution"><p>In presence of acidic medium, ionisation of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">H</mi><mn>2</mn></msub><mi mathvariant="normal">S</mi></math> is supressed so less number of <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi mathvariant="normal">S</mi><mrow><mn>2</mn><mo>-</mo></mrow></msup></math> ions are produced. So only those sulphides are precipitated which have low solubility product <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><msub><mi mathvariant="normal">K</mi><mi>sp</mi></msub></mfenced></math> value.</p><p>Thus, in acidic medium, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">H</mi><mn>2</mn></msub><mi mathvariant="normal">S</mi></math> is very feebly ionised giving very small concentration of sulphide ion for precipitation. Therefore, the most insoluble salts <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>CuS</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>HgS</mi></math> are precipitated.</p></div>


tags: ['Chemistry', 'Practical Chemistry', 'BITSAT', 'BITSAT 2010']
answer: <div class="solution">$\operatorname{CoS}$ is not precipitated in acidic medium.</div>
source_db: MarksBatch2_P4.db
title:
when-h-2-s-gas-is-passed-through-the-hcl-containing-aqueous-solution-of-cucl-2-hgcl-2-bicl-3-and-cocl-2-it-does-not-precipitate-out

slug:
when-h-2-s-gas-is-passed-through-the-hcl-containing-aqueous-solution-of-cucl-2-hgcl-2-bicl-3-and-cocl-2-it-does-not-precipitate-out-15443

question:
<div class="question">When $\mathrm{H}_{2} \mathrm{~S}$ gas is passed through the $\mathrm{HCl}$ containing aqueous solution of $\mathrm{CuCl}_{2}, \mathrm{HgCl}_{2}$, $\mathrm{BiCl}_{3}$ and $\mathrm{CoCl}_{2}$ it does not precipitate out</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{CuS}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{HgS}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{Bi}_{2} \mathrm{~S}_{3}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\mathrm{CoS}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{CoS}$</span> </div>


title: when-light-is-refracted-which-of-the-following-does-not-change
slug: when-light-is-refracted-which-of-the-following-does-not-change-43680
question: <div class="question">When light is refracted, which of the following does not change ?</div>
tags: ['Physics', 'Ray Optics', 'BITSAT', 'BITSAT 2013']
answer: <div class="solution">Frequency does not change on refraction.</div>
source_db: MarksBatch2_P4.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Wavelength</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Frequency</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Velocity</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Amplitude</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Frequency</span> </div>


title: when-nh-3-is-passed-over-heated-metal-a-its-amide-is-formed-the-metal-is
slug: when-nh-3-is-passed-over-heated-metal-a-its-amide-is-formed-the-metal-is-57131
tags: ['Chemistry', 'p Block Elements (Group 15, 16, 17 & 18)', 'BITSAT', 'BITSAT 2013']
source_db: MarksBatch2_P4.db
question:
<div class="question">When $\mathrm{NH}_{3}$ is passed over heated metal $\mathrm{A}$, its amide is formed. The metal is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{Mg}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\mathrm{K}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{Al}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{Pb}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{K}$</span> </div>

answer:
<div class="solution">When Potassium is treated with ammonia, then potassium amide is obtained
<br/> <br/>$\mathrm{K}+\mathrm{NH}_{3} \longrightarrow \underset{\text { Pot. amide }}{\mathrm{KNH}_{2}}+\frac{1}{2} \mathrm{H}_{2}$</div>


tags: ['Physics', 'Dual Nature of Matter', 'BITSAT', 'BITSAT 2018']
source_db: MarksBatch2_P4.db
title:
when-photon-of-energy-4-0-ev-strikes-the-surface-of-a-metal-a-the-elected-photoelectrons-have-maximum-kinetic-energy-t-a-ev-and-debroglie-wavelength-a

slug:
when-photon-of-energy-4-0-ev-strikes-the-surface-of-a-metal-a-the-elected-photoelectrons-have-maximum-kinetic-energy-t-a-ev-and-debroglie-wavelength-a-94271

question:
<div class="question">When photon of energy <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>0</mn><mo> </mo><mi>eV</mi></math> strikes the surface of a metal <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math>, the elected photoelectrons have maximum kinetic energy <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>T</mi><mi>A</mi></msub><mo> </mo><mi>eV</mi></math> and de-Broglie wavelength <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>λ</mi><mi>A</mi></msub></math>. The maximum kinetic energy of photoelectron liberated from another metal <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math> by photon of energy <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>50</mn><mo> </mo><mi>eV</mi></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>T</mi><mi>B</mi></msub><mo>=</mo><mfenced><mrow><msub><mi>T</mi><mi>A</mi></msub><mo>-</mo><mn>1</mn><mo>.</mo><mn>50</mn></mrow></mfenced><mo> </mo><mi>eV</mi></math>. If the de-Broglie wavelength of these photoelectrons <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>λ</mi><mi>B</mi></msub><mo>=</mo><mn>2</mn><msub><mi>λ</mi><mi>A</mi></msub></math>, then choose the correct statement(s).</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">The work function of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>50</mn><mo> </mo><mi>eV</mi></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">The work function of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>0</mn><mo> </mo><mi>eV</mi></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>T</mi><mi>A</mi></msub><mo>=</mo><mn>3</mn><mo>.</mo><mn>2</mn><mo> </mo><mi>eV</mi></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">All of the above</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">The work function of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>0</mn><mo> </mo><mi>eV</mi></math></span> </div>

answer:
<div class="solution"><p>From Einstein photoelectric equation,<br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mo>=</mo><msub><mi>ϕ</mi><mn>0</mn></msub><mo>+</mo><msub><mi>KE</mi><mi>max</mi></msub></math></p><p>For metal <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>  </mo><mn>4</mn><mo>=</mo><msub><mi>ϕ</mi><mi>A</mi></msub><mo>+</mo><msub><mi>T</mi><mi>A</mi></msub><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><mfenced><mi mathvariant="normal">i</mi></mfenced></math><br/>For metal <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>5</mn><mo>=</mo><msub><mi>ϕ</mi><mi>B</mi></msub><mo>+</mo><mfenced><mrow><msub><mi>T</mi><mi>A</mi></msub><mo>-</mo><mn>1</mn><mo>.</mo><mn>5</mn></mrow></mfenced><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><mfenced><mi>ii</mi></mfenced></math></p><p>From Eq. (i) and (ii), wo got<br/><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>ϕ</mi><mi>B</mi></msub><mo>-</mo><msub><mi>ϕ</mi><mi>A</mi></msub><mo>=</mo><mn>2</mn></math></p><p>Now, according to de-Broglie hypothesis,<br/><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>λ</mi><mi>A</mi></msub><mo>=</mo><mfrac><mi>h</mi><mrow><mi>m</mi><mi>v</mi></mrow></mfrac><mo>=</mo><mfrac><mi>h</mi><msqrt><mn>2</mn><mi>m</mi><msub><mi>T</mi><mi>A</mi></msub></msqrt></mfrac></math></p><p>Similarly, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>λ</mi><mi>B</mi></msub><mo>=</mo><mfrac><mi>h</mi><msqrt><mn>2</mn><mi>m</mi><msub><mi>T</mi><mi>B</mi></msub></msqrt></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mo> </mo><mfrac><msub><mi>λ</mi><mi>A</mi></msub><msub><mi>λ</mi><mi>B</mi></msub></mfrac><mo>=</mo><msqrt><mfrac><msub><mi>T</mi><mi>B</mi></msub><msub><mi>T</mi><mi>A</mi></msub></mfrac></msqrt><mo>=</mo><msqrt><mfrac><mrow><msub><mi>T</mi><mi>A</mi></msub><mo>-</mo><mn>1</mn><mo>.</mo><mn>5</mn></mrow><msub><mi>T</mi><mi>A</mi></msub></mfrac></msqrt><mo>=</mo><msup><mfenced><mrow><mn>1</mn><mo>-</mo><mfrac><mrow><mn>1</mn><mo>.</mo><mn>5</mn></mrow><msub><mi>T</mi><mi>A</mi></msub></mfrac></mrow></mfenced><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mfrac><mn>1</mn><mn>2</mn></mfrac></mfenced><mn>2</mn></msup><mo>=</mo><mn>1</mn><mo>-</mo><mfrac><mrow><mn>1</mn><mo>.</mo><mn>5</mn></mrow><msub><mi>T</mi><mi>A</mi></msub></mfrac></math></p><p>On solving, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>T</mi><mi>A</mi></msub><mo>=</mo><mn>2</mn><mo>.</mo><mn>0</mn><mi>eV</mi></math></p><p>or <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>ϕ</mi><mi>A</mi></msub><mo>=</mo><mn>4</mn><mo>-</mo><msub><mi>T</mi><mi>A</mi></msub><mo>=</mo><mn>4</mn><mo>-</mo><mn>2</mn><mo>=</mo><mn>2</mn><mo>.</mo><mn>0</mn><mi>eV</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>ϕ</mi><mi>B</mi></msub><mo>=</mo><mn>6</mn><mo>-</mo><msub><mi>T</mi><mi>A</mi></msub><mo>=</mo><mn>6</mn><mo>-</mo><mn>2</mn><mo>=</mo><mn>4</mn><mo>.</mo><mn>0</mn><mi>eV</mi></math></p></div>


title: when-rain-is-accompanied-by-a-thunderstorm-the-collected-rain-water-will-have-a-ph-value-1
slug: when-rain-is-accompanied-by-a-thunderstorm-the-collected-rain-water-will-have-a-ph-value-1-12298
tags: ['Chemistry', 'Environmental Chemistry', 'BITSAT', 'BITSAT 2014']
source_db: MarksBatch2_P4.db
question:
<div class="question">When rain is accompanied by a thunderstorm, the collected rain water will have a $\mathrm{pH}$ value:</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Slightly lower than that of rain water without thunderstorm.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Slightly higher than that when the thunderstorm is not there.</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Uninfluenced by occurrence of thunderstorm.</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Which depends upon the amount of dust in air.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Slightly lower than that of rain water without thunderstorm.</span> </div>

answer:
<div class="solution">Normal rain water has pH 5.6. Thunderstorm results in the formation $\mathrm{NO}$ and $\mathrm{HNO}_{3}$ which lowers the $\mathrm{pH}$</div>


tags: ['Chemistry', 'd and f Block Elements', 'BITSAT', 'BITSAT 2013']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">1: 1</span> </div>
source_db: MarksBatch2_P4.db
title:
when-same-amount-of-zinc-is-treated-separately-with-excess-of-sulphuric-acid-and-excess-of-sodium-hydroxide-solution-the-ratio-of-volumes-of-hydrogen-

slug:
when-same-amount-of-zinc-is-treated-separately-with-excess-of-sulphuric-acid-and-excess-of-sodium-hydroxide-solution-the-ratio-of-volumes-of-hydrogen-10904

question:
<div class="question">When same amount of zinc is treated separately with excess of sulphuric acid and excess of sodium hydroxide solution, the ratio of volumes of hydrogen evolved is:</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">1: 1</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">1: 2</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">2: 1</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">9: 4</span> </li> </ul>

answer:
<div class="solution">$\mathrm{Zn}+\mathrm{H}_{2} \mathrm{SO}_{4} \rightarrow \mathrm{ZnSO}_{4}+\mathrm{H}_{2}$
<br/> <br/>$\mathrm{Zn}+2 \mathrm{NaOH} \rightarrow \mathrm{Na}_{2} \mathrm{ZnO}_{2}+\mathrm{H}_{2}$
<br/> <br/>$\therefore$ Ratio of volumes of $\mathrm{H}_{2}$ evolved is 1: 1</div>


title: when-the-first-ionisation-energies-are-plotted-against-atomic-number-the-peaks-are-occupied-by
tags: ['Chemistry', 'Classification of Elements and Periodicity in Properties', 'BITSAT', 'BITSAT 2013']
source_db: MarksBatch2_P4.db
slug:
when-the-first-ionisation-energies-are-plotted-against-atomic-number-the-peaks-are-occupied-by-72178

question:
<div class="question">When the first ionisation energies are plotted against atomic number, the peaks are occupied by</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Alkali metals</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Rare gases</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Halogens</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Transition elements</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Rare gases</span> </div>

answer:
<div class="solution">Rare gases; as the $\mathrm{e}^{-}$ is to be removed from stable configuration.</div>


tags: ['Chemistry', 'Thermodynamics (C)', 'BITSAT', 'BITSAT 2018']
source_db: MarksBatch2_P4.db
title:
when-the-heat-of-a-reaction-at-constant-pressure-is-25-10-3-cal-and-entropy-change-for-the-reaction-is-7-4-cal-deg-1-it-is-predicted-that-the-reaction

slug:
when-the-heat-of-a-reaction-at-constant-pressure-is-25-10-3-cal-and-entropy-change-for-the-reaction-is-7-4-cal-deg-1-it-is-predicted-that-the-reaction-60861

question:
<div class="question">When the heat of a reaction at constant pressure is <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>25</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo> </mo><mi>cal</mi></math> and entropy change for the reaction is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>.</mo><mn>4</mn><mo> </mo><mi>cal</mi><mo> </mo><msup><mo>deg</mo><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>, it is predicted that the reaction at <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mn>25</mn><mn>0</mn></msup><mi mathvariant="normal">C</mi></math> is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">revesible</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">spontaneous</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">non-spontaneous</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">irreversible</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">spontaneous</span> </div>

answer:
<div class="solution"><p>Heat at constant pressure means enthalpy. i.e., <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ΔG</mi><mo>=</mo><mi>ΔH</mi><mo>-</mo><mi>TΔS</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ΔH</mi><mo>=</mo><mn>2</mn><mo>.</mo><mn>5</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup><mi>cal</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ΔS</mi><mo>=</mo><mn>7</mn><mo>.</mo><mn>4</mn><msup><mi>caldeg</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">T</mi><mo>=</mo><mn>298</mn><mo> </mo><mi mathvariant="normal">K</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ΔG</mi><mo>=</mo><mi>ΔH</mi><mo>-</mo><mi>TΔS</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mo>-</mo><mn>25</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup><mo>-</mo><mn>298</mn><mo>×</mo><mn>7</mn><mo>.</mo><mn>4</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mo>-</mo><mn>4705</mn><mo>.</mo><mn>2</mn><mo> </mo><mi>cal</mi></math></p><p>As the value of ΔG is −4705.2 cal, which is a negative value, so this reaction will be spontaneous. </p><p>Hence, the process is spontaneous.</p></div>


tags: ['Chemistry', 'Electrochemistry', 'BITSAT', 'BITSAT 2009']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">(b)</span> </div>
source_db: MarksBatch2_P4.db
title:
when-the-sample-of-copper-with-zinc-impurity-is-to-be-purified-by-electrolysis-the-appropriate-electrodes-are-1

slug:
when-the-sample-of-copper-with-zinc-impurity-is-to-be-purified-by-electrolysis-the-appropriate-electrodes-are-1-90615

question:
<div class="question">When the sample of copper with zinc impurity is to be purified by electrolysis, the appropriate electrodes are<br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/4GyCFcJebA3DzfjQuoykkTTgsoLDUNfK5tgDrPvxLrQ.original.fullsize.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">(a)</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">(b)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">(c)</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">(d)</span> </li> </ul>

answer:
<div class="solution">In electrolytic purification cathode is of pure metal and anode is of impure metal. At anode: $\mathrm{M} \rightarrow \mathrm{M}^{\mathrm{n}+}+\mathrm{n} \overline{\mathrm{e}}$<br/>At cathode: $\mathrm{M}^{\mathrm{n}+}+\mathrm{n} \overline{\mathrm{e}} \rightarrow \mathrm{M}$.<br/>The pure metal is thus deposited at cathode.</div>


title: when-the-temperature-is-raised-the-viscosity-of-liquid-decreases-this-is-because
slug: when-the-temperature-is-raised-the-viscosity-of-liquid-decreases-this-is-because-65721
tags: ['Chemistry', 'States of Matter', 'BITSAT', 'BITSAT 2010']
answer: <div class="solution">No Solution available</div>
source_db: MarksBatch2_P4.db
question:
<div class="question">When the temperature is raised, the viscosity of liquid decreases this is because</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">decreased volume of the solution.</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">increased attraction between molecules.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">decreased covalent and hydrogen bond forces.</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">increase in temperature increase the average kinetic energy of molecules which overcomes the attractive force between them.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">increased attraction between molecules.</span> </div>


title: which-alkene-on-ozonolysis-gives-ch-3-ch-2-cho-and
slug: which-alkene-on-ozonolysis-gives-ch-3-ch-2-cho-and-55302
tags: ['Chemistry', 'Hydrocarbons', 'BITSAT', 'BITSAT 2012']
source_db: MarksBatch2_P4.db
question:
<div class="question">Which alkene on ozonolysis gives $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CHO}$ and
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/nHrNRO4k0pu_zL-a5vZFUnI_yJtMUloxcIlKehQTjuY.original.fullsize.png"/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/v3LqiF7qr235LTyMytKhToW8KfFaAFp46mKgykKPl6U.original.fullsize.png"/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}=\mathrm{CHCH}_{2} \mathrm{CH}_{3}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}=\mathrm{CHCH}_{3}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/-Ff6UjeisJMVP80aq_xWOXYRQmnDggC18iNqY7OqxHA.original.fullsize.png"/></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/v3LqiF7qr235LTyMytKhToW8KfFaAFp46mKgykKPl6U.original.fullsize.png"/></span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/FRa4kTtZ_rgJHyTWwkjzR42zf9tN_K5GcJyllSACFvo.original.fullsize.png"/></div>


title: which-among-the-following-actinoids-does-not-have-stable-electronic-configuration
slug: which-among-the-following-actinoids-does-not-have-stable-electronic-configuration-29664
tags: ['Chemistry', 'd and f Block Elements', 'BITSAT', 'BITSAT 2018']
source_db: MarksBatch2_P4.db
question:
<div class="question">Which among the following actinoids does not have stable electronic configuration</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Protactinium</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Nobelium</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Americium</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Lawrencium</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Protactinium</span> </div>

answer:
<div class="solution"><p>Protactinium <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mi>Pa</mi></mfenced></math> is the element that does not have stable electronic configuration.</p><p>Protactinium <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mi>Pa</mi></mfenced><mo>=</mo><mfenced close="]" open="["><mi>Rn</mi></mfenced><mn>5</mn><msup><mi mathvariant="normal">f</mi><mn>2</mn></msup><mn>6</mn><msup><mi mathvariant="normal">d</mi><mn>1</mn></msup><mn>7</mn><msup><mi mathvariant="normal">s</mi><mn>2</mn></msup></math> (Atomic number <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>91</mn></math>)</p><p>Nobelium <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mi>No</mi></mfenced><mo>=</mo><mfenced><mi>Rn</mi></mfenced><mn>5</mn><msup><mi mathvariant="normal">f</mi><mn>14</mn></msup><mn>6</mn><msup><mi mathvariant="normal">d</mi><mn>0</mn></msup><mn>7</mn><msup><mi mathvariant="normal">s</mi><mn>2</mn></msup></math> (Atomic number <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>102</mn></math>)</p><p>Lawrencium <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mi>Lr</mi></mfenced><mo>=</mo><mfenced close="]" open="["><mi>Rn</mi></mfenced><mn>5</mn><msup><mi mathvariant="normal">f</mi><mn>14</mn></msup><mn>6</mn><msup><mi mathvariant="normal">d</mi><mn>1</mn></msup><mn>7</mn><msup><mi mathvariant="normal">s</mi><mn>2</mn></msup></math> (Atomic number <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>103</mn></math>)</p><p>Americium <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mi>Am</mi></mfenced><mo>=</mo><mfenced close="]" open="["><mi>Rn</mi></mfenced><mn>5</mn><msup><mi mathvariant="normal">f</mi><mn>7</mn></msup><mn>6</mn><msup><mi mathvariant="normal">d</mi><mn>0</mn></msup><mn>7</mn><msup><mi mathvariant="normal">s</mi><mn>2</mn></msup></math> (Atomic number <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>95</mn></math>)</p></div>


title: which-among-the-following-is-not-an-antibiotic
slug: which-among-the-following-is-not-an-antibiotic-72497
question: <div class="question">Which among the following is not an antibiotic?</div>
tags: ['Chemistry', 'Chemistry in Everyday Life', 'BITSAT', 'BITSAT 2014']
source_db: MarksBatch2_P4.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Penicillin</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Oxytocin</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\quad$ Ofloxacin</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Tetracycline</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Oxytocin</span> </div>

answer:
<div class="solution">Oxytocin is a hormone (nanopetide) which contracts uterus after the child birth and produces lactation in the mammary glands.</div>


title: which-compound-has-antifluorite-structure
slug: which-compound-has-antifluorite-structure-10042
question: <div class="question">Which compound has antifluorite structure?</div>
tags: ['Chemistry', 'Solid State', 'BITSAT', 'BITSAT 2022']
source_db: MarksBatch2_P4.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"> <br/>$\mathrm{MnO}_4$
<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"> <br/>$\mathrm{Na}_2 \mathrm{O}$
<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"> <br/>$\mathrm{Na}_2 \mathrm{O}_2$
<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"> <br/>$\mathrm{Li}_2 \mathrm{O}_2$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"> <br/>$\mathrm{Na}_2 \mathrm{O}$
<br/></span> </div>

answer:
<div class="solution">Anti-fluorite structure refers to an anion array with tetrahedral cations and the compound having $A_2 B$ formula have anti-fluorite structure. So, $\mathrm{Na}_2 \mathrm{O}$ has an anti-fluorite structure in which $\mathrm{Na}^{+}$ions occupy all the tetrahedral voids and $\mathrm{O}^{2-}$occupy half of the cubic holes.</div>


title: which-form-coloured-salts
slug: which-form-coloured-salts-88321
question: <div class="question">Which form coloured salts:</div>
tags: ['Chemistry', 'd and f Block Elements', 'BITSAT', 'BITSAT 2014']
source_db: MarksBatch2_P4.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Non-metals</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Metals</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">p-block elements</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">Transitional elements</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Transitional elements</span> </div>

answer:
<div class="solution">Most of the transition metal compounds (ionic as well as covalent) are coloured both in the solid state and in aqueous solution in contrast to the compounds of $s$ and $p$ -block elements due to the presence of incomplete d-subshell.</div>


title: which-is-not-the-correct-statement-at-nos-ce-58-lu-71-la-57-yb-70-1
slug: which-is-not-the-correct-statement-at-nos-ce-58-lu-71-la-57-yb-70-1-99558
tags: ['Chemistry', 'd and f Block Elements', 'BITSAT', 'BITSAT 2020']
answer: <div class="solution">Option(a) is incorrect as $\mathrm{Yb}^{3+}$ is colorless.</div>
source_db: MarksBatch2_P4.db
question:
<div class="question">Which is not the correct statement? (At. nos. $\mathrm{Ce}=58, \mathrm{Lu}=71, \mathrm{La}=57, \mathrm{Yb}=70$ )</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Colour of $\mathrm{Yb}^{3+}$ ion is pink.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{La}^{3+}$ is diamagnetic.</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{Ce}^{4+}$ has $f^{0}$ configuration.</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{Lu}^{3+}$ had $f^{14}$ configuration.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Colour of $\mathrm{Yb}^{3+}$ ion is pink.</span> </div>


tags: ['Chemistry', 'Thermodynamics (C)', 'BITSAT', 'BITSAT 2015']
source_db: MarksBatch2_P4.db
title:
which-law-of-the-thermodynamics-helps-in-calculating-the-absolute-entropies-of-various-substances-at-different-temperatures

slug:
which-law-of-the-thermodynamics-helps-in-calculating-the-absolute-entropies-of-various-substances-at-different-temperatures-19502

question:
<div class="question">Which law of the thermodynamics helps in calculating the absolute entropies of various substances at different temperatures?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">First law</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Second law</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Third law</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Zeroth law</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Third law</span> </div>

answer:
<div class="solution">The third law helps to calculate the absolute entropies of pure substances at different temperature. The entropy of the substance at different temperature. $\mathrm{T}$ may be calculated by the measurement of heat capacity change
<br/> <br/>$$
<br/> <br/>\begin{array}{l}
<br/> <br/>\mathrm{S}_{\mathrm{T}}-\mathrm{S}_{0}=\Delta \mathrm{S}=\int_{0}^{\mathrm{T}} \frac{\mathrm{C}_{\mathrm{p}} \mathrm{dt}}{\mathrm{T}} \\
<br/> <br/>\text { Where } \mathrm{S}_{\mathrm{T}}=\text { Entropy at } \mathrm{T} \mathrm{K}
<br/> <br/>\end{array}
<br/> <br/>$$
<br/> <br/>$\mathrm{S}_{0}=$ Entropy at $0 \mathrm{~K}$
<br/> <br/>$$
<br/> <br/>\begin{array}{l}
<br/> <br/>=\mathrm{C}_{\mathrm{p}} \cdot \log _{e} \mathrm{~T} \\
<br/> <br/>=2.303 \mathrm{C}_{\mathrm{p}} \mathrm{log} \mathrm{T}
<br/> <br/>\end{array}
<br/> <br/>$$</div>


title: which-liberates-ammonia-when-treated-with-water
slug: which-liberates-ammonia-when-treated-with-water-76775
question: <div class="question">Which liberates ammonia when treated with water?</div>
tags: ['Chemistry', 'p Block Elements (Group 15, 16, 17 & 18)', 'BITSAT', 'BITSAT 2010']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">All</span> </div>
source_db: MarksBatch2_P4.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{Li}_{3} \mathrm{~N}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{Mg}_{3} \mathrm{~N}_{2}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{CaCN}_{2}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">All</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

answer:
<div class="solution">All nitrides react with $\mathrm{H}_{2} \mathrm{O}$ to give $\mathrm{NH}_{3}$ and $\mathrm{CaCN}_{2}$ also react with $\mathrm{H}_{2} \mathrm{O}$<br/>$$<br/>\mathrm{CaNCN}+3 \mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{CaCO}_{3}+\mathrm{NH}_{3}<br/>$$</div>


title: which-method-is-useful-for-the-synthesis-of-ether
slug: which-method-is-useful-for-the-synthesis-of-ether-93386
question: <div class="question">Which method is useful for the synthesis of ether?</div>
tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 1)']
source_db: MarksBatch2_P4.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/tSoOL9nbEQBEy_WMHyZyYpvsJ3aOAenGI2DETSszfcw.original.fullsize.png"/><br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/9oQA_3SnkeTQmz2rYrfhrkWmu2I1nocuv0byD_BwwA0.original.fullsize.png"/><br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/WopTivWTZSTJ33Lpc5OcqR3OMrYfIM637PLhBg0kDUo.original.fullsize.png"/><br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/w75e7Y41IvnfD5x0iAb39jNWqkOHJhuh5tkEedJWgyk.original.fullsize.png"/><br/></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/WopTivWTZSTJ33Lpc5OcqR3OMrYfIM637PLhBg0kDUo.original.fullsize.png"/><br/></span> </div>

answer:
<div class="solution">At $443 \mathrm{~K}$ compound in (d) will produce propene. In (a) alkene will be produced as tertiary halide and strong base favours elimination. In (b) reaction is not possibie at room temperature as due to resonance $\mathrm{C}-\mathrm{Cl}$ bond has partial double bond character which is very difficult to break.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/2AuvY8-6Y3dUmcXp294WYEtau_-xpJNQ894yuDhNTFU.original.fullsize.png"/><br/></div>


title: which-of-the-following-0-1-m-aqueous-solution-will-have-lowest-freezing-point
slug: which-of-the-following-0-1-m-aqueous-solution-will-have-lowest-freezing-point-50984
tags: ['Chemistry', 'Solutions', 'BITSAT', 'BITSAT 2018']
source_db: MarksBatch2_P4.db
question:
<div class="question">Which of the following <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>1</mn><mo> </mo><mi mathvariant="normal">M</mi></math> aqueous solution will have lowest freezing point?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Potassium sulphate</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Sodium chloride</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Urea</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Glucose</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Potassium sulphate</span> </div>

answer:
<div class="solution"><p>Potassium sulphate <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><msub><mi mathvariant="normal">K</mi><mn>2</mn></msub><msub><mi>SO</mi><mn>4</mn></msub></mrow></mfenced><mo>,</mo><mo> </mo><mi mathvariant="normal">i</mi><mo>=</mo><mn>3</mn></math></p><p>Sodium chloride <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mi>NaCl</mi></mfenced><mo>,</mo><mo> </mo><mi mathvariant="normal">i</mi><mo>=</mo><mn>2</mn></math></p><p>Urea, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">i</mi><mo>=</mo><mn>1</mn></math></p><p>Glucose, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">i</mi><mo>=</mo><mn>1</mn></math></p><p>Greater the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">i</mi></math>, greater lowering in freezing point and hence, lower will be the freezing temperature.</p><p>Therefore, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">K</mi><mn>2</mn></msub><msub><mi>SO</mi><mn>4</mn></msub></math> solution has the lowest freezing point.</p></div>


title: which-of-the-following-according-to-lechateliers-principle-is-correct
slug: which-of-the-following-according-to-lechateliers-principle-is-correct-94286
question: <div class="question">Which of the following according to LeChatelier's principle is correct?</div>
tags: ['Chemistry', 'Chemical Equilibrium', 'BITSAT', 'BITSAT 2015']
source_db: MarksBatch2_P4.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Increase in temperature favours the endothermic reaction</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Increase in temperature favours the exothermic reaction</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Increase in pressure shifts the equilibrium in that side in which number of gaseous moles increases</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">All of the above are true</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Increase in temperature favours the endothermic reaction</span> </div>

answer:
<div class="solution">According to Le-Chatelier's principle increase in temperature favours the endothermic reaction while decrease in temperature favour the exothermic reaction. Increase in pressure shifts the equilibrium in that side in which number of gaseous moles decreases.</div>


title: which-of-the-following-acts-as-an-antioxidant-in-edible-oils
slug: which-of-the-following-acts-as-an-antioxidant-in-edible-oils-95084
question: <div class="question">Which of the following acts as an antioxidant in edible oils?</div>
tags: ['Chemistry', 'Biomolecules', 'BITSAT', 'BITSAT 2021']
answer: <div class="solution">Vitamin $\mathrm{E}$ is an antioxidant present in edible oils.</div>
source_db: MarksBatch2_P4.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Vitamin B</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Vitamin C</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Vitamin D</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">Vitamin E</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Vitamin E</span> </div>


title: which-of-the-following-acts-as-the-stationary-phase-in-paper-chromatography
slug: which-of-the-following-acts-as-the-stationary-phase-in-paper-chromatography-22706
tags: ['Chemistry', 'General Organic Chemistry', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 2)']
source_db: MarksBatch2_P4.db
question:
<div class="question">Which of the following acts as the stationary phase in paper chromatography?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>Water</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>Alumina</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>Silica gel</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>None of these</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>Water</span> </div>

answer:
<div class="solution">Chromatography paper contains water trapped in it, which acts as the stationary phase.</div>


title: which-of-the-following-among-alkalimetal-is-most-reactive
slug: which-of-the-following-among-alkalimetal-is-most-reactive-87502
question: <div class="question">Which of the following among alkalimetal is most reactive?</div>
tags: ['Chemistry', 's Block Elements', 'BITSAT', 'BITSAT 2014']
answer: <div class="solution">Amongst alkali metals, Cs is most reactive because of its lowest IE.</div>
source_db: MarksBatch2_P4.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{Na}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{K}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{Rb}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\mathrm{Cs}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{Cs}$</span> </div>


title: which-of-the-following-are-isoelectronic-species-i-c-h-3-ii-nh-2-iii-nh-4-iv-nh-3
slug: which-of-the-following-are-isoelectronic-species-i-c-h-3-ii-nh-2-iii-nh-4-iv-nh-3-95822
tags: ['Chemistry', 'Chemical Bonding and Molecular Structure', 'BITSAT', 'BITSAT 2017']
source_db: MarksBatch2_P4.db
question:
<div class="question"><p>Which of the following are isoelectronic species?</p><p>I. <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi mathvariant="normal">C</mi><mo>+</mo></mover><msub><mi mathvariant="normal">H</mi><mn>3</mn></msub></math></p><p>II. <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi>NH</mi><mn>2</mn><mo>-</mo></msubsup></math></p><p>III. <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi>NH</mi><mn>4</mn><mo>+</mo></msubsup></math></p><p>IV. <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>NH</mi><mn>3</mn></msub></math></p></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">I</mi><mo>,</mo><mo> </mo><mi>II</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>III</mi></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>II</mi><mo>,</mo><mo> </mo><mi>III</mi></math><span style="background-color:null;"> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>IV</mi></math></span></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">I</mi><mo>,</mo><mo> </mo><mi>II</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>IV</mi></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>II</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">I</mi></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>II</mi><mo>,</mo><mo> </mo><mi>III</mi></math><span style="background-color:null;"> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>IV</mi></math></span></span> </div>

answer:
<div class="solution"><p>I. Number of electrons in <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi mathvariant="normal">C</mi><mo>+</mo></mover><msub><mi mathvariant="normal">H</mi><mn>3</mn></msub><mo>=</mo><mn>6</mn><mo>+</mo><mn>3</mn><mo>-</mo><mn>1</mn><mo>=</mo><mn>8</mn></math></p><p>II. Number of electrons in <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi>NH</mi><mn>2</mn><mo>-</mo></msubsup><mo>=</mo><mn>7</mn><mo>+</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo>=</mo><mn>10</mn></math></p><p>III. Number of electrons in <math xmlns="http://www.w3.org/1998/Math/MathML"><msubsup><mi>NH</mi><mn>4</mn><mo>+</mo></msubsup><mo>=</mo><mn>7</mn><mo>+</mo><mn>4</mn><mo>-</mo><mn>1</mn><mo>=</mo><mn>10</mn></math></p><p>IV. Number of electrons in <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>NH</mi><mn>3</mn></msub><mo>=</mo><mn>7</mn><mo>+</mo><mn>3</mn><mo>=</mo><mn>10</mn></math></p><p>Since, species with same number of electrons are called isoelectronic species, Hence, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>IInd</mi><mo>,</mo><mi>IIIrd</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>IVth</mi></math> are isoelectronic.</p></div>


tags: ['Chemistry', 'Coordination Compounds', 'BITSAT', 'BITSAT 2016']
answer: <div class="solution">No Solution</div>
source_db: MarksBatch2_P4.db
title:
which-of-the-following-arrangements-does-not-represent-the-correct-order-of-the-property-stated-against-it-1

slug:
which-of-the-following-arrangements-does-not-represent-the-correct-order-of-the-property-stated-against-it-1-70312

question:
<div class="question">Which of the following arrangements does not represent the correct order of the property stated against it?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\mathrm{V}^{2+}&lt;\mathrm{Cr}^{2+}&lt;\mathrm{Mn}^{2+}&lt;\mathrm{Fe}^{2+}$ :paramagnetic
<br/> <br/>behaviour</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{Ni}^{2+}&lt;\mathrm{Co}^{2+}&lt;\mathrm{Fe}^{2+}&lt;\mathrm{Mn}^{2+}:$ ionic size</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{Co}^{3+}&lt;\mathrm{Fe}^{3+}&lt;\mathrm{Cr}^{3+}&lt;\mathrm{Sc}^{3+}:$ stability in
<br/> <br/>aqueous solution</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{Sc}&lt;\mathrm{Ti}&lt;\mathrm{Cr}&lt;\mathrm{Mn}:$ number of oxidation states</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{V}^{2+}&lt;\mathrm{Cr}^{2+}&lt;\mathrm{Mn}^{2+}&lt;\mathrm{Fe}^{2+}$ :paramagnetic
<br/> <br/>behaviour</span> </div>


title: which-of-the-following-can-be-used-to-prevent-the-decomposition-of-h-2-o-2-1
slug: which-of-the-following-can-be-used-to-prevent-the-decomposition-of-h-2-o-2-1-31370
tags: ['Chemistry', 'Hydrogen', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 2)']
source_db: MarksBatch2_P4.db
question:
<div class="question">Which of the following can be used to prevent the decomposition of $\mathrm{H}_2 \mathrm{O}_2$ ?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>Urea</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>Formaldehyde</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>Formic acid</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>Ethanol</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>Urea</span> </div>

answer:
<div class="solution">Urea acts as stablising agent. It prevents the decomposition of $\mathrm{H}_2 \mathrm{O}_2$.</div>


tags: ['Chemistry', 'Chemistry in Everyday Life', 'BITSAT', 'BITSAT 2014']
answer: <div class="solution">No Solution</div>
source_db: MarksBatch2_P4.db
title:
which-of-the-following-can-possibly-be-used-as-analgesic-without-causing-addiction-and-modification-1

slug:
which-of-the-following-can-possibly-be-used-as-analgesic-without-causing-addiction-and-modification-1-80526

question:
<div class="question">Which of the following can possibly be used as analgesic without causing addiction and modification?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">morphine</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\mathrm{N}$ -acetyl-para-aminophenol</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">diazepam</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">tetrahydrocatenol</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{N}$ -acetyl-para-aminophenol</span> </div>


title: which-of-the-following-cannot-give-iodometric-titration
slug: which-of-the-following-cannot-give-iodometric-titration-10374
question: <div class="question">Which of the following cannot give iodometric titration?</div>
tags: ['Chemistry', 'Redox Reactions', 'BITSAT', 'BITSAT 2011']
answer: <div class="solution">There is no reaction between $\mathrm{I}^{-}$ and $\mathrm{Fe}^{3+}$.</div>
source_db: MarksBatch2_P4.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\mathrm{Fe}^{3+}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{Cu}^{2+}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{Pb}^{2+}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{Ag}^{2+}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{Fe}^{3+}$</span> </div>


title: which-of-the-following-catalyst-is-used-in-preparation-of-high-density-polythene
slug: which-of-the-following-catalyst-is-used-in-preparation-of-high-density-polythene-51249
tags: ['Chemistry', 'Polymers', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 2)']
source_db: MarksBatch2_P4.db
question:
<div class="question">Which of the following catalyst is used in preparation of high density polythene?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>Peroxide catalyst</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>Ziegler - Natta catalyst</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>Wilkinson's catalyst</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>Pd - catalyst</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>Ziegler - Natta catalyst</span> </div>

answer:
<div class="solution">High density polythene is formed when addition polymerisation of ethene takes place in a hydrocarbon solvent in presence of catalyst such as Ziegler-Natta catalyst.</div>


tags: ['Chemistry', 'Chemistry in Everyday Life', 'BITSAT', 'BITSAT 2021']
source_db: MarksBatch2_P4.db
title:
which-of-the-following-chemicals-can-be-added-for-sweetening-of-food-items-at-cooking-temperature-and-does-not-provides-calories

slug:
which-of-the-following-chemicals-can-be-added-for-sweetening-of-food-items-at-cooking-temperature-and-does-not-provides-calories-26223

question:
<div class="question">Which of the following chemicals can be added for sweetening of food items at cooking temperature and does not provides calories?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Sucrose</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Glucose</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Aspartame</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">Sucralose</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Sucralose</span> </div>

answer:
<div class="solution">Sucralose is trichloro derivative of sucrose. It is stable at cooking temperture. It does not provide calories.</div>


title: which-of-the-following-combinations-of-properties-would-be-most-desirable-for-a-cooking-pot
slug: which-of-the-following-combinations-of-properties-would-be-most-desirable-for-a-cooking-pot-71923
tags: ['Physics', 'Thermal Properties of Matter', 'BITSAT', 'BITSAT 2009']
answer: <div class="solution">No Solution available</div>
source_db: MarksBatch2_P4.db
question:
<div class="question">Which of the following combinations of properties would be most desirable for a cooking pot?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">High specific heat and low conductivity.</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Low specific heat and high conductivity.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">High specific heat and high conductivity.</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Low specific heat and low conductivity.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Low specific heat and high conductivity.</span> </div>


title: which-of-the-following-combinations-would-not-result-in-the-formation-of-a-buffer-solution
slug: which-of-the-following-combinations-would-not-result-in-the-formation-of-a-buffer-solution-88891
tags: ['Chemistry', 'Ionic Equilibrium', 'BITSAT', 'BITSAT 2012']
source_db: MarksBatch2_P4.db
question:
<div class="question">Which of the following combinations would not result in the formation of a buffer solution?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{NH}_{3}+\mathrm{HCl}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{NH}_{4} \mathrm{Cl}+\mathrm{NH}_{3}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{CH}_{3} \mathrm{COOH}+\mathrm{NaCl}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\mathrm{NaOH}+\mathrm{CH}_{3} \mathrm{COOH}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{NaOH}+\mathrm{CH}_{3} \mathrm{COOH}$</span> </div>

answer:
<div class="solution">Combination of $\mathrm{NaOH}$ and $\mathrm{CH}_{3} \mathrm{COOH}$ is the mixture of alkali and acetic acid. Therefore this combination can not be buffer forming solution.</div>


title: which-of-the-following-compound-can-not-be-used-in-preparation-of-iodoform
slug: which-of-the-following-compound-can-not-be-used-in-preparation-of-iodoform-52399
tags: ['Chemistry', 'Aldehydes and Ketones', 'BITSAT', 'BITSAT 2009']
source_db: MarksBatch2_P4.db
question:
<div class="question">Which of the following compound can not be used in preparation of iodoform?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{CH}_{3} \mathrm{CHO}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{CH}_{3} \mathrm{COCH}_{3}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\mathrm{HCHO}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">2 -propanol</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{HCHO}$</span> </div>

answer:
<div class="solution">Formaldehyde can not produce <img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/uUH4ygZrSdDkmLjuHI3M1VaCcESWb8Td_FqAMkcUk0U.original.fullsize.png"/><br/>-group<br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/j5dVCgKIWkEUWWPdAVj-dfeukyUem20CXhmW_WxayYo.original.fullsize.png"/><br/><br/>on reaction with<br/>potassium iodide and sod. hypochlorite vield iodoform.</div>


title: which-of-the-following-compound-does-not-follow-huckels-rule
slug: which-of-the-following-compound-does-not-follow-huckels-rule-89197
question: <div class="question">Which of the following compound does not follow Huckel's rule? </div>
tags: ['Chemistry', 'General Organic Chemistry', 'BITSAT', 'BITSAT 2017']
source_db: MarksBatch2_P4.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><p><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/182262fe-3b28-4b37-84d2-e3ef3b5fcdad-image.png" style="width: 120px; height: 117px;"/></p></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><p><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/428ee751-8502-4036-96f9-c63da75d26a7-image.png" style="width: 80px; height: 136px;"/></p></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><p><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/9f500ce5-02c3-4032-a466-c58eda08a125-image.png" style="width: 100px; height: 117px;"/></p></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><p><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/1be4d869-fd86-42c5-9c0b-9a0d3cce09c8-image.png" style="width: 100px; height: 104px;"/></p></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><p><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/1be4d869-fd86-42c5-9c0b-9a0d3cce09c8-image.png" style="width: 100px; height: 104px;"/></p></span> </div>

answer:
<div class="solution"><p>An aromatic compound can follow Huckel's rule if it has <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>4</mn><mi mathvariant="normal">n</mi><mo>+</mo><mn>2</mn><mo>)</mo><mi mathvariant="normal">π</mi></math>-electrons</p><p>where, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">n</mi><mo>=</mo></math> integer <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mo>…</mo></math> etc.</p><p>Thus, </p><p>(a) <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">n</mi><mo>=</mo><mn>0</mn><mo>;</mo><mo> </mo><mn>4</mn><mo>×</mo><mn>0</mn><mo>+</mo><mn>2</mn><mo>=</mo><mn>2</mn><mi mathvariant="normal">π</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> follow Huckel's rule</p><p>(b) <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">n</mi><mo>=</mo><mn>1</mn><mo>;</mo></math> Number of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">π</mi></math>-electrons <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>6</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> follows Huckels rules.</p><p>(c) <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">n</mi><mo>=</mo><mn>1</mn><mo>;</mo></math> Number of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">π</mi></math>-electrons <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>6</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math> follows Huckel's rule.</p><p>(d) <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">n</mi><mo>=</mo><mn>1</mn></math>, Number of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">π</mi></math>-electrons <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>8</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>4</mn><mi mathvariant="normal">n</mi><mo>+</mo><mn>2</mn><mo>=</mo><mn>4</mn><mo>×</mo><mn>1</mn><mo>+</mo><mn>2</mn><mo>=</mo><mn>6</mn><mo>)</mo></math></p><p>but this compound has <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math> electrons which distorts the plane and hence does not follows Huckel's rule.</p></div>


title: which-of-the-following-compound-has-all-the-four-types-1-2-3-and-4-of-carbon-atoms
slug: which-of-the-following-compound-has-all-the-four-types-1-2-3-and-4-of-carbon-atoms-27864
tags: ['Chemistry', 'General Organic Chemistry', 'BITSAT', 'BITSAT 2016']
source_db: MarksBatch2_P4.db
question:
<div class="question">Which of the following compound has all the four types $\left(1^{\circ}, 2^{\circ}, 3^{\circ}\right.$ and $\left.4^{\circ}\right)$ of carbon atoms?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">2,3,4 -Trimethylpentane</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">neo-Pentane</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">2,2,4 -Trimethylpentane</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of the three</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">2,2,4 -Trimethylpentane</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/16fn6fJh1ZkQRvxLgyxWSLUmIpVMoZPpLsPR7UteAZU.original.fullsize.png"/><br/> <br/> <br/>$\mathrm{C}_{1}$ and $\mathrm{C}_{5}$ are $1^{\circ}, \mathrm{C}_{3}$ is $2^{\circ}, \mathrm{C}_{4}$ is $3^{\circ},$ and $\mathrm{C}_{2}$ is $4^{\circ}$</div>


title: which-of-the-following-compound-is-not-chiral-1
slug: which-of-the-following-compound-is-not-chiral-1-29311
question: <div class="question">Which of the following compound is not chiral?</div>
tags: ['Chemistry', 'General Organic Chemistry', 'BITSAT', 'BITSAT 2011']
source_db: MarksBatch2_P4.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\mathrm{DCH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{Cl}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{CH}_{3} \mathrm{CHDCH}_{2} \mathrm{Cl}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{CH}_{3} \mathrm{CHClCH}_{2} \mathrm{D}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CHDCl}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{DCH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{Cl}$</span> </div>

answer:
<div class="solution">None of the carbon atoms in $\mathrm{DCH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{Cl}$ is chiral i.e., each carbon<br/>atom is achiral (symmetric).</div>


title: which-of-the-following-compound-is-obtained-by-heating-ammonium-cyanate
slug: which-of-the-following-compound-is-obtained-by-heating-ammonium-cyanate-53499
tags: ['Chemistry', 'p Block Elements (Group 15, 16, 17 & 18)', 'BITSAT', 'BITSAT 2009']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">Urea</span> </div>
source_db: MarksBatch2_P4.db
question:
<div class="question">Which of the following compound is obtained by heating ammonium cyanate?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Alkane</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Urea</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Ethylamine</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Ammonium thiocyanate</span> </li> </ul>

answer:
<div class="solution">Urea is obtained by heating ammonium cyanate<br/>$$<br/>\mathrm{NH}_{4} \mathrm{CNO} \stackrel{\Delta}{\longrightarrow} \mathrm{NH}_{2} \mathrm{CONH}_{2}<br/>$$<br/>Ammonium cyanate Urea</div>


title: which-of-the-following-compound-will-give-blood-red-colour-while-doing-the-lassaignes-test-for-n
tags: ['Chemistry', 'General Organic Chemistry', 'BITSAT', 'BITSAT 2018']
source_db: MarksBatch2_P4.db
slug:
which-of-the-following-compound-will-give-blood-red-colour-while-doing-the-lassaignes-test-for-n-56123

question:
<div class="question">Which of the following compound will give blood red colour while doing the Lassaigne's test for <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">N</mi></math>.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mfenced><msub><mi>NH</mi><mn>2</mn></msub></mfenced><mn>2</mn></msub><mi mathvariant="normal">C</mi><mo>=</mo><mi mathvariant="normal">O</mi></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">H</mi><mn>2</mn></msub><mi mathvariant="normal">N</mi><mfenced><mrow><msub><mi mathvariant="normal">C</mi><mn>6</mn></msub><msub><mi mathvariant="normal">H</mi><mn>4</mn></msub></mrow></mfenced><msub><mi>SO</mi><mn>3</mn></msub><mi mathvariant="normal">H</mi></math></p></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">C</mi><mn>6</mn></msub><msub><mi mathvariant="normal">H</mi><mn>5</mn></msub><msub><mi>SO</mi><mn>3</mn></msub><mi mathvariant="normal">H</mi></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>CHCl</mi><mn>3</mn></msub></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">H</mi><mn>2</mn></msub><mi mathvariant="normal">N</mi><mfenced><mrow><msub><mi mathvariant="normal">C</mi><mn>6</mn></msub><msub><mi mathvariant="normal">H</mi><mn>4</mn></msub></mrow></mfenced><msub><mi>SO</mi><mn>3</mn></msub><mi mathvariant="normal">H</mi></math></p></span> </div>

answer:
<div class="solution"><p>When nitrogen and sulphur both are present in the organic compound, they combine during fusion to form sodium thiocyanate (sulphocyanide).</p><p>Thus, the compounds containing both <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">N</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">S</mi></math> give blood red colour in Lassaigne's test due to the formation of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Fe</mi><msub><mfenced><mi>SCN</mi></mfenced><mn>2</mn></msub></math>. Thus, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">H</mi><mn>2</mn></msub><mi mathvariant="normal">N</mi><mfenced><mrow><msub><mi mathvariant="normal">C</mi><mn>6</mn></msub><msub><mi mathvariant="normal">H</mi><mn>4</mn></msub></mrow></mfenced><msub><mi>SO</mi><mn>3</mn></msub><mi mathvariant="normal">H</mi></math> gives blood red colour in Lassaigne's test of nitrogen.</p></div>


